estudo da organização da turbulência na interface - BDTD

INSTITUTO NACIONAL DE PESQUISAS DA AMAZÔNIA - INPA
UNIVERSIDADE DO ESTADO DO AMAZONAS - UEA
CURSO DE PÓS-GRADUAÇÃO EM CLIMA E AMBIENTE
ESTUDO DA ORGANIZAÇÃO DA TURBULÊNCIA NA INTERFACE
FLORESTA-ATMOSFERA: ANÁLISES DE DADOS OBSERVACIONAIS E
SIMULAÇÃO NUMÉRICA
CLÉO QUARESMA DIAS JÚNIOR
Manaus, Amazonas
Julho, 2015
CLÉO QUARESMA DIAS JÚNIOR
ESTUDO DA ORGANIZAÇÃO DA TURBULÊNCIA NA INTERFACE
FLORESTA-ATMOSFERA: ANÁLISES DE DADOS OBSERVACIONAIS E
SIMULAÇÃO NUMÉRICA.
DR. EDSON PEREIRA MARQUES FILHO - orientador
DR LEONARDO DEANE DE ABREU SÁ - co-orientador
Tese apresentada ao Instituto Nacional de Pesquisas
da Amazônia e Universidade do Estado do Amazonas,
como parte dos requisitos para obtenção do título de
Doutor em Clima e Ambiente.
Manaus, Amazonas
Julho, 2015
ii
D541
Dias Júnior, Cléo Quaresma
Estudo da organização da turbulência na interface florestaatmosfera: análises de dados observacionais e simulação numérica /
Cléo Quaresma Dias Júnior. --- Manaus: [s.n.], 2015.
107 p. : il.
Tese (Doutorado) --- INPA/UEA, Manaus, 2015.
Orientadores: Edson Pereira Marques Filho.
Coorientador: Leonardo Deane de Abreu Sá.
Área de concentração : Clima e Ambiente.
1. Ventos. 2. Large eddy simulation. 3. Turbulência. I. Título.
CDD 551.518
iii
Sinopse:
Estudaram-se aspectos do arrasto superficial e suas consequências em escoamentos acima
de florestas densas, a detecção de estruturas coerentes, a existência de diferentes regimes
turbulência noturnos e a simulação do escoamento turbulento através do “Large Eddy
Simulation”.
Palavras-chave: Floresta Amazônica, Ponto de Inflexão, Perfis de vento, Estruturas
Coerentes, LES, Transformada Wavelet.
Manaus, Amazonas
Julho, 2015
iv
Para minha esposa, Mary
Barroso Dias, minha princesa
Maria Eduarda Barroso Dias
e meus queridos pais Cléo
Quaresma Dias e Sebastiana
do Socorro Almeida.
v
AGRADECIMENTOS
Ao Dr. Leonardo Deane de Abreu Sá que nestes 10 anos de convivência, além de ter
me ensinado valiosos conhecimentos a respeito do “fazer ciência”, me mostrou como é ser um
cientista e um homem ético, honesto e um servidor público que exerce com extrema
probidade sua função.
Ao Dr. Edson Pereira Marques Filho pela paciência nos ensinamentos computacionais,
nas orientações, nas motivações científicas. Além do que lhe sou muito grato à logística
computacional oferecida para o uso do LES.
Aos professores do CLIAMB, em especial ao Dr. Antônio Manzi, Dra. Rita Valéria e
ao Dr. Luiz Candido pela transmissão de valiosos conhecimentos.
Ao Dr. Luiz Candido que sempre se mostrou muito solícito no que se refere ao uso do
supercomputador do INPA.
A banca avaliadora que prontamente se dispôs a participar desta defesa.
Ao Instituto Nacional de Pesquisas da Amazônia (INPA) e Universidade do Estado do
Amazonas (UEA) através do Programa de Pós-Graduação em Clima e Ambiente (CLIAMB).
A CAPES palas bolsas de doutorado e “Ciência sem Fronteiras” que me permitiram
conhecer e interagir com diferentes cientistas de outros países.
Ao Dr. Matthias Mauder pela receptividade quando estive na Alemanha e pela
infraestrutura oferecida ao desenvolvimento de parte desta pesquisa.
Ao Projeto LBA pelos dados disponíveis.
A todos os colegas de turma, em especial ao Raoni, Elisa, Paulo Coutinho, Stefan pelo
companheirismo durante esses quatro anos.
vi
Aos amigos de residência em Manaus, Francisco, Cledenilson e Claudomiro pelo
apoio motivacional.
vii
“Se você encontrar um caminho
sem obstáculos, ele provavelmente
não leva a lugar nenhum.”
(Frank Clark)
viii
RESUMO
Investigou-se a estrutura do escoamento turbulento acima da reserva florestal RebioJarú, localizada no Estado de Rondônia. Para isso, utilizaram-se dados medidos em torre
micrometeorológica, coletados durante a estação úmida, em períodos diurnos e noturnos, e
também se recorreu à modelagem numérica usando-se Large Eddy Simulation (LES).
Para condições diurnas foram analisados alguns aspectos do perfil vertical do vento
médio acima e no interior do dossel florestal. Usou-se satisfatoriamente a função tangente
hiperbólica com o objetivo de se obter um ajuste para o perfil vertical do vento acima e no
interior do dossel florestal, o qual levou em conta a variabilidade da altura do ponto de
inflexão no perfil vertical do vento e o índice de área foliar. Além disso, obteve-se uma
relação linear robusta entre a variabilidade da altura do ponto de inflexão e a escala temporal
associada à organização das estruturas coerentes existentes imediatamente acima da copa
florestal.
Para a camada limite noturna foram analisadas ocorrências de três diferentes regimes
turbulentos: regime 1) fraca turbulência e baixa velocidade do vento; regime 2) forte
turbulência e alta velocidade do vento e regime 3) eventos turbulentos não estacionários.
Notou-se que na camada limite noturna amazônica a maior frequência de ocorrência é do
regime 1 (95%), comparada aos regimes 2 e 3 (5% cada). Contudo, para situações do regime
2, observou-se que o fluxo de calor sensível é cerca de 40 vezes maior comparativamente às
situações em que o regime 1 é dominante. Além do quê, em situações em que predomina o
regime 2, observou-se que a altura do ponto de inflexão, a escala de comprimento de
cisalhamento do vento, as escalas temporais das estruturas coerentes e a taxa de dissipação de
energia cinética turbulenta foram consideravelmente maiores quando comparados aos
respectivos valores obtidos no regime 1, indicando a ocorrência de forte mistura turbulenta na
camada limite superficial. Também constatou-se que os episódios classificados como regime
3 foram essencialmente não-estacionários.
Na aplicação do LES foi acrescentada uma força de arrasto no modelo, representativa
da floresta amazônica, com o objetivo de se ter simulações o mais próximo da realidade. Seu
objetivo foi o de investigar a ocorrência das estruturas coerentes acima da floresta amazônica.
Os resultados mostraram que o escoamento turbulento foi sensível à presença do dossel
florestal, com um nítido ponto de inflexão no perfil vertical do vento logo acima do dossel.
Além disso, os perfis do fluxo de momento e de energia cinética turbulenta foram similares
àqueles obtidos com dados experimentais. Na região entre 1h e 4h (onde h corresponde à
ix
altura média do dossel florestal) os valores de várias grandezas aí observadas, tais como
pressão, fluxo de momento, skewnesses de componentes de velocidade do vento e vorticidade
sugerem que as estruturas coerentes se organizam na forma de rolos, com eixo de simetria
perpendicular ao escoamento médio. Os resultados reforçam a importância de se considerar a
física do ponto de inflexão no perfil vertical de velocidade do vento nas trocas turbulentas
entre floresta e atmosfera.
x
ABSTRACT
Were investigated the structure of turbulent flow above the Rebio-Jarú forest reserve,
located in the state of Rondônia. For this, we used data measured in micrometeorological
tower, collected during the wet season, in daytime and nighttime periods, and also performed
numerical modeling using Large Eddy Simulation (LES).
For daytime conditions some aspects of the average vertical wind profile above and
within the forest canopy were analyzed. It is used the hyperbolic tangent function
satisfactorily in order to obtain a functional shape for the vertical wind profile above and
inside the canopy, which took into account the variability of the height of the inflection point
in the vertical wind profile and the leaf area index, too. Furthermore, we obtained a robust
linear relationship between the varying height of the inflection point and the characteristic
time scale associated with the coherent organization of existing structures immediately above
the forest canopy.For the nocturnal boundary layer situations, three different turbulent
regimes were analyzed: regime 1) weak turbulence and low wind speed; regime 2) strong
turbulence and high wind speed and regime 3) non-stationary turbulent events. It was noted
that in the nocturnal boundary layer the highest frequency of occurrence is related with the
first regime (95%), compared to regimes 2 and 3 (5% each). However, for regime-2’s
situations, it was observed that the sensible heat flux is about 40 times higher compared to
situations in which the regime 1 is dominant. Besides, in situations where the regime 2 is
predominant, it was observed that the height of the inflection point, the
length-scale
associated with the wind-shear, the coherent structures’ time scale, and the dissipation rate of
turbulent kinetic energy were significantly higher when compared to the respective values
obtained in the regime 1, indicating the occurrence of strong turbulent mixing in the surface
boundary layer in such situations. In addition, it was found that the episodes classified as
regime 3 were essentially non-stationary.
In applying LES was added a drag force into the model, representative of the
rainforest canopy, in order to obtain simulations closer to reality. Its main goal was to
investigate the occurrence of coherent structures above the Amazon rainforest. The results
showed that the turbulent flow was sensitive to the presence of the forest canopy, with a welldefined inflection point on the vertical wind profile just above the canopy. Furthermore, the
profiles of momentum flux and turbulent kinetic energy were similar to those obtained with
experimental data. In the region between 1h and 4h (where h is the average height of the
forest canopy) the observed values of several physical variables such as pressure, momentum
xi
fluxes, skewnesses of the wind velocity components, and vorticity are suggesting that
coherent structures are organized in form of rolls, with symmetry axis perpendicular to the
mean flow. The results reinforce the importance of considering the physical role of the
inflection point on the vertical wind speed profile in the turbulent exchanges between forest
and atmosphere.
xii
SUMÁRIO
Resumo ...................................................................................................................
...................................................................................................................
Abstract
Lista de
figuras .....................................................................................................................
...................................................................................................................
Introdução
Objetivo ...................................................................................................................
Capítulo 1 Coherent structures detected in the unstable atmospheric surface
layer above the Amazon Forest…………………………………………..
1.1 Introduction…………………………………………………………………
1.2 Experimental and methods…………………………………………………
1.2.1 Site and data................................................................................................
1.2.2 Meteorological conditions………………………………………………….
1.2.3 Data quality control…………………………………………………….......
1.2.4 Methods…………………………………………………………………….
1.3 Results………………………………………………………………………
1.4 Conclusion…………………………………………….……………………
Capítulo 2 An empirical-analytic model to describe the vertical wind speed profile
above and within amazon forest………………………………….
2.1 Introduction………………………………………………………………....
2.2 Material and methods……………………………………………………….
2.2.1 Experimental site…………………………………………………………….
2.2.2 Dataset…………………………………………………………………….....
2.2.3 Theoretical elements and methodology…………………………………….
2.3 Results…………………………………………………………………….....
2.4. Conclusions…………………………………………………………………
Capítulo 3 Turbulence regimes in the stable boundary layer above and within the
Amazon forest……………………………………………………………..
3.1 Introduction………………………………………………………………...
3.2 Experimental Setup and dataset…………………………………………..
3.3 Methods………………………………………………………………….....
Inflection point height in the wind profile and wind shear's length-scale
3.3.1 (𝐿ℎ )………………………………………………………………………….
3.3.2 Turbulent kinetic energy dissipation…………………………………….....
3.3. 3 Time scale of coherent structure .. .………………………………………....
3.3.4 Stationary conditions…………………………………………………….....
3.4 Results………………………………………………………………………
3.4.1 Turbulent regimes………………………………………………………......
3.4.2 Sensible heat flux…………………………………………………………...
3.4.3 Inflection point height, wind shear and dissipation length scale………….
3.4.4 Time scale of coherent structures…………………………………………..
3.4.5 Case study………………………………………………………………......
3.4.5.1 Continuous profiles of temperature, relative humidity and wind speed…..
3.4.5.2 Temperature, relative humidity and wind speed profiles…………………..
3.5 Discussion………………………………………………………………......
3.6 Conclusions…………………………………………………………………
Capítulo 4 LES applied to analyze the turbulent flow organization above amazon
forest………………………………………………………………………...
4.1 Introduction………………………………………………………………….
p.viii
p.x
p.xiv
p.1
p.6
p.8
p.8
p.10
p.10
p.12
p.14
p.14
p.18
p.23
p.30
p.30
p.31
p.31
p.33
p.33
p.36
p.43
p.48
p.48
p.50
p.52
p.52
p.53
p.53
p.54
p.55
p.55
p.58
p.59
p.61
p.62
p.62
p.65
p.67
p.69
p.77
p.77
xiii
4.2
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.4.6
4.4.7
4.5.
Conclusões.
Experimental data…………………………………………………………...
Numerical methods………………………………………………………….
Numerical implementation………………………………………………....
Canopy structure……………………………………………………………
Initial and boundary conditions…………………………………………....
Results……………………………………………………………………....
Mean statistical fields above the Amazon rainforest………………………
Sweeps and ejections………………………………………………………..
Efficiency of momentum transport…………………………………………
Moments of third order for the wind speed………………………………..
Standard deviation of pressure…………………………………………….
Vorticity………………………………………………………………….....
Discussion…………………………………………………………………..
Conclusions………………………………………………………………....
……………………………………………………………………………....
p.79
p.80
p.80
p.82
p.83
p.84
p.84
p.87
p.89
p.90
p.92
p.93
p.94
p.96
p.103
xiv
LISTA DE FIGURAS
Capítulo 1
Fig 1 Meteorological tower erected at Rebio-Jaru forest reserve……………….
Fig 2 Fast response instruments in the meteorological tower at Rebio-Jaru…..
Fig 3 Cup anemometers ranged at different heights in the meteorological tower
at Rebio-Jaru………………………………………………………………..
Fig 4 Histogram of frequency of wind direction for observations of the
intervals: (a) from 11:00 to 16:00 local-time and (b) from 20:00 up to 9:00
local-time…………………………………………………………………...
Fig 5 Total precipitation for Julian days: 41 to 51 and 55-67………………….
Fig 6 Scale variance of the wavelets coefficients as a function of the time scale,
for virtual temperature time series obtained from 09:00 h - 09:30 h, local
time, 10 February , 1999……………………………………………………
Fig 7 Third degree polynomial best fitting for the vertical wind speed profile
(low response wind speed data measured from 15:30 h -16:00 h, on 19
February, 1999……………………………………………………………...
Fig 8 Vertical profile of dimensionless wind velocity for a partially overcast
sky…………………………………………………………………………..
Fig 9 Evolution of the coherent structures time-scale hourly-mean values (a) and
the vertical wind profile inflection point height (b), along with their
standard deviations, obtained above Rebio-Jarú forest reserve, for 144
available half-hourly data sets……………………………………………...
Fig 10 Comparison of the evolution of the inflection point height and the
coherent structures time-scale above Rebio-Jarú forest reserve……………
Fig 11 Comparison between the inflection point height and the coherent structure
time-scale for 144 run data for day-time conditions……………………….
Fig 12 Comparison of two time-scales: coherent structure time scale (y-axis) and
inflection point time-scale (x-axis) for 144 half-hourly data sets…………
Capítulo 2
Fig 1 Micrometeorological tower built on the Jarú Reserve……………………..
Fig 2 Profile of the nine anemometers installed in the Jarú Reserve
micrometeorological tower…………………………………………………..
Fig 3 The observed vertical mean wind profile compared with the one provided
by the Hyperbolic model (Julian day 46; from 08:00 a.m. to 09:00 a.m.)…
Fig 4 Modeled wind profiles for different values of the (β) parameter…………..
Fig 5 Modeled wind profiles for different values of the (γ) parameter…………..
Fig 6 Daytime hourly variation of inflection point height (solid line) and gamma
values
(dashed
line)
for
the
Rebio-Jarú
reserve……………………………………
Fig 7 Modelled wind profiles for different parameter values: a) alpha; b) beta; c)
gamma; d) mu; e) omega; and e) LAI….......................................................
Fig 8 Modelled wind profiles for two different values of LAI (4.2: dashed grey
line and 5.8: black solid line), which correspond to the seasonal extreme
values in the Amazon forest………………………………………………..
Fig 9 Observed mean wind profile and associated standard deviation compared
with hyperbolic tangent function fitted data (second version)…………….
Capítulo 3
Fig 1 a) Photograph of the meteorological tower erected in the Rebio-Jarú forest
p.11
p.12
p.12
p.14
p.14
p.16
p.17
p.18
p.19
p.19
p.20
p.21
p.32
p.33
p.37
p.37
p.38
p.39
p.40
p.41
p.42
p.51
xv
Fig 2
Fig 3
Fig 4
Fig 5
Fig 6
Fig 7
Fig 1
Fig 2
Fig 3
Fig 4
Fig 5
Fig 6
Fig 7
Fig 8
Fig 9
Fig 10
reserve; b) schematic diagram showing the sonic and cup anemometers
arranged on the tower and their relationship to the forest canopy………..
Standard deviation of the vertical velocity (𝜎𝑤 ), a characteristic turbulent
velocity scale as a function of the wind speed measured at 67 m height,
corresponding at 14 nights. Black, blue and red circles correspond
respectively to regime 1 (low wind and weak turbulence), regime 2 (high
wind and strong turbulence) and regime 3 (intermittent turbulence
events)………………………………………………………………………
Similar to Fig 2. Black circles and green dots correspond, respectively to
stationary 5min periods and non-stationary 5min period………………….
Probability Density Functions (PDFs) for: a) Inflection point height, 𝑧𝑖 ,
(m); b) Wind shear length-scale, 𝐿ℎ , (m); c) logarithm of the viscous
dissipation, 𝜀, (m2 s-3). Dashed lines correspond to regime 1’s occurrences
and full lines correspond to regime’s 2 ones……………………………….
The same of the Fig. 4 but for the coherent strucuture time scale
correspond to: a) horizontal wind velocity streamwise componente, 𝑢; b)
vertical wind velocity component, 𝑤; c) temperature, 𝑇. Dashed lines
correspond to regime 1’s occurrences and full lines correspond to
regime’s 2 ones……………………………………………………………..
Contour plots regarding the evolution of: a) Temperature; b) relative
humidity and c) wind speed for a case study concerning the turbulent
regime 2 (Julian day 45 from 21:30 to 21:50 local time)…………………..
5 min-vertical profiles of a) mean temperature (𝑇1 ) for the earliest 5 min
of the regime 2’s event; b) the same but the latest 5 min mean temperature
(𝑇2 ) of the same event. 𝑇2 – 𝑇1 values; d, e and f) the same for the a, b and
c graphics, but for the relative humidity……………………………………
Capítulo 4
Picture showing the meteorological tower built at Rebio Jarú forest
reserve and the surrounding vegetation…………………………………….
Vertical Profile of leaf area density of the Rebio Jarú forest reserve (for
LAI = 5.0): Found by Marques Filho et at. (2005) (gray region) and
modifications inserted in the LES used in this work (black line)………….
Vertical profiles of (a) virtual potential temperature (𝜃𝑣 ); (b) specific
humidity (q); (c) horizontal velocity components; used as initial condition
in the LES…………………………………………………………………..
Vertical profile: a) of horizontal wind speed and b) of turbulent kinetic
energy. Both normalized by the fiction velocity calculated at canopy top.
Vertical profile: a) standard deviation of the streamwise velocity (dashed
line) and standard deviation of the vertical velocity (solid line) and b) of
momentum flux. Both normalized by the fiction velocity calculated at
canopy top………………………………………………………………….
Flux ratio: momentum flux by sweep ( 𝑤 ′ < 0 𝑒 𝑢′ > 0) to that by
ejection (𝑤 ′ > 0 𝑒 𝑢′ < 0)…………………………………………………
Vertical profile of correlation coeficiente between u e w (𝑟𝑤𝑢 )……………
Vertical profiles of skewness of u (dotted line) and w (solid line)…………
Vertical profile of standard deviation of pressure normalized by 𝑢∗ ............
Vertical profile of vorticity in the x, y and z directions…………………….
p.56
p.57
p.60
p.62
p.64
p.67
p.80
p.82
p.84
p.85
p.87
p.89
p.90
p.92
p.93
p.94
1
INTRODUÇÃO
Os estudos de escoamentos turbulentos acima de florestas apresenta considerável
complexidade quando comparado com aquele da interação entre superfícies “lisas”,
homogêneas e a atmosfera (Mahrt et al., 1994; Högström e Bergström, 1996; Raupach et al.,
1996; Brunet e Irvine, 2000; Kruijt et al., 2000; Mahrt, 2000). Esta complexidade tem
estimulado a realização de intensas pesquisas para compreender melhor a dinâmica do
escoamento atmosférico acima do dossel florestal e seu grau de acoplamento com o
escoamento no interior da cobertura vegetal.
Dentre os principais processos aerodinâmicos presentes acima de florestas pode-se
destacar o intenso cisalhamento do vento, que induz o surgimento de um ponto de inflexão no
perfil de velocidade do vento (PI), logo acima da altura media da copa (Raupach et al., 1996;
Mahrt et al., 2000). O surgimento de um PI é inevitável quando ocorre absorção de momento
em um espaço verticalmente estendido, como o que acontece acima de florestas (Finnigan,
2000). Análise de estabilidade linear e não-linear deste PI prevê uma sequência de autovalores
instáveis, primeiro em duas e, em seguida, em três dimensões. A instabilidade inicial, linear, é
uma onda de Kelvin-Helmholtz, o que pode ser interpretado como regiões de perturbações
positivas e negativas na vorticidade, com um comprimento de onda λ que é proporcional à
espessura da vorticidade, (Finnigan et al., 2009). A análise não linear mostra que a
vorticidade da onda pode evoluir para vórtices de amplitude finita que apresentam eixos de
simetria transversais à direção do escoamento médio, com o comprimento de onda original λ
(Stewart, 1969).
A existência de um PI gera instabilidades hidrodinâmicas no escoamento turbulento,
dificultando sua representação sobre florestas em termos da Teoria da Similaridade de MoninObukhov (TSMO) (Brunet e Irvine, 2000). Esta camada turbulenta próxima a superfícies
rugosas, conhecida como subcamada rugosa (SR), exige novas interpretações físicas para
explicar fenômenos que ai ocorrem, particularmente alguns não lineares (Py et al., 2004;
Campanharo et al., 2008; Belusic e Mahrt, 2012). Além disso, na SR, os grandes vórtices
turbulentos apresentam uma dinâmica, escala e energia determinadas pela instabilidade do PI
(Finnigan, 2000).
Thomas e Foken (2007) procuraram definir uma “altura aerodinâmica do dossel” e
consideraram-na como sendo zx, a altura do ponto de inflexão no perfil do vento médio (API).
Para determinar zx, eles ajustaram os dados dos perfis verticais de vento disponíveis a um
polinômio de terceira ordem. Este método, sugerido originalmente por Raupach et al. (1996),
2
parece razoável e está consistente com a idéia do perfil de vento logarítmico sobre o dossel e
exponencial dentro deste, desde que se considere a existência de uma região intermediária, a
SR, na qual os perfis de velocidade média do vento apresentam características especiais,
muito diferentes daquelas previstas pela TSMO.
Pontos de inflexão no perfil de vento acima da floresta Amazônica, em Rondônia, já
foram investigados por diferentes autores (Pachêco, 2001; Sá e Pachêco, 2006; Dias-Júnior et
al., 2013). Os resultados destes estudos constataram que a altura do ponto de inflexão varia
durante o dia e que esta constitui um parâmetro de escala importante na obtenção de relações
gerais para o perfil do vento acima e dentro do dossel. Sá e Pachêco (2006) propuseram uma
nova relação para o perfil vertical da velocidade do vento acima e no interior da floresta. Eles
usaram informações da posição do ponto de inflexão e da velocidade do vento na altura de sua
ocorrência, bem como uma escala de comprimento associada ao cisalhamento vertical do
vento na altura média da copa florestal. Resultados de Marshall et al. (2002), para simulação
do escoamento acima de vegetação em túnel de vento, mostraram grande concordância com
os resultados de Sá e Pachêco (2006), ainda que eles não tenham levado em conta a
possibilidade de variação do API, como estes últimos autores propuseram. Dias-Júnior et al.
(2013) sugeriram que a variação do API pode trazer como consequência a variação da escala
temporal de ocorrência de estruturas coerentes (ECs) no campo térmico, fenômeno
extremamente concernente aos fluxos turbulentos de calor sensível (Paw U et al., 1992).
Em relação às ECs, é importante mencionar que vários pesquisadores já mostraram
que elas contribuem de forma decisiva para os fluxos turbulentos de calor sensível e de
momento (Turner et al., 1994; Högström e Bergström, 1996; Thomas e Foken, 2007; Eder et
al., 2013). No entanto, poucos estudos abordaram a questões da dinâmica do escoamento nas
proximidades do dossel da floresta amazônica, e o impacto delas nos processos de troca em
geral. Além disso, na interface floresta-atmosfera algumas características peculiares do
escoamento atmosférico podem ser relevantes na formação de tais estruturas, como por
exemplo: a instabilidade do ponto de inflexão (Robinson, 1991; Raupach et al., 1996; Brunet
e Irvine, 2000; Finnigan, 2000), curto-circuito espectral (Cava e Katul, 2008), variabilidade
sazonal no índice de área foliar (Doughty et al., 2008) com possíveis consequências no arrasto
superficial, variabilidade espacial das concentrações de carbono e fluxos de CO2 ao longo de
regiões planas, declives e vales na floresta (Araújo et al., 2010).
Para se chegar aos objetivos propostos neste trabalho recorreu-se, além da utilização
de dados experimentais, à simulação dos grandes turbilhões (Large Eddy Simulation - LES).
É importante mencionar que dentre as muitas vantagens do LES, uma delas é a de permitir
3
uma melhor compreensão da estrutura da turbulência em alturas não alcançadas pelas torres
micrometeorológicas. Além do quê, o LES permite a investigação de características espaciais
do escoamento turbulento, o que dificilmente poderia ser realizado apenas com medidas em
situ.
As análises dos dados experimentais possibilitaram a melhor compreensão de algumas
características do escoamento turbulento, tanto para a camada limite convectiva (CLC) quanto
para a camada limite noturna (CLN) amazônicas.
Para a CLC, analisou-se uma escala temporal associada com o API. Observou-se que
há uma estreita correlação entre as escalas temporais das ECs e do API. Tal resultado permite
a obtenção de novos “insights” sobre a instabilidade do ponto de inflexão, além de
proporcionar um melhor entendimento das principais características dos vórtices turbulentos
acima de florestas altas. Além disso, usou-se a função tangente hiperbólica para parametrizar
o perfil vertical do vento, acima e dentro da floresta, usando-se para tanto alguns parâmetros
chaves, tal com o API e o índice de área foliar, como os propostos por Yi (2008).
Para a CLN a complexidade do escoamento turbulento se acentua, uma vez que sob
tais situações muitos fenômenos associados à estratificação estável podem tornar o
escoamento mais complexo, como é o caso da existência de ondas internas de gravidade (Zeri
e Sá, 2011), ventos catabáticos (Princevac et al., 2008), correntes de densidade (Sun et al.,
2002), instabilidades de Kelvin-Helmholtz (Zhang et al., 2001), jatos de baixos níveis (Poulos
et al., 2002), dentre outros. No caso do escoamento acima de vegetação alta, ainda há o fator
complicador associado à existência da SR (Williams et al., 2007).
Outra questão relevante nos estudos da CLN é o da caracterização dos regimes
turbulentos noturnos e problemas correlatos (Mahrt, 1998, 1999; Acevedo e Fitzjarrald, 2003;
Cava et al., 2004; Van de Wiel et al., 2002a, 2002b, 2003; Acevedo et al., 2009; Sun et al.,
2012). Estudos recentes aplicados a sítios experimentais da Amazônia, Uatumã (a nordeste do
estado do Amazonas) e da Rebio-Jarú (a nordeste do estado de Rondônia), mostraram
diferenças significativas no que concerne: i) à ocorrência de ondas de gravidade, à influência
de nuvens nas grandezas escalares do escoamento, à existência de maior ou menor
estacionariedade (Zeri et al., 2014) e a existência de diferentes regimes de turbulência
noturnos (Cava et al., 2004; Sun et al., 2012); ii) à variabilidade sazonal dos fluxos e
concentrações de CO2 acima da floresta de Uatumã em função do regime de turbulência
existente (Mafra, 2014).
Um dos principais objetivos deste trabalho foi investigar aspectos cíclicos da CLN
(Van de Wiel et al., 2002a, 2002b, 2003), no que tange a classificação e caracterização de
4
regimes turbulentos. Contudo, há duas questões importantes abordadas nessa tese: i) a
relevância de fenômenos noturnos na atmosfera tropical acima de continente; ii) as
características da turbulência acima de uma floresta singular pela sua extensão, povoada por
árvores altas como é o caso da floresta amazônica. Nesta condição, em mais de 90 % do
tempo os ventos são fracos e o transporte turbulento também é fraco. Contudo, em curtos
intervalos de tempo, da ordem de dezenas de minutos, durante os quais aumenta o caráter
estacionário das flutuações turbulentas, ocorrem eventos de vento forte com intenso transporte
turbulento, o que muda o caráter das trocas turbulentas entre floresta-atmosfera. Pouca
atenção tem sido dada aos estudos destes eventos intensos. Os resultados aqui apresentados
são contrários a ideia frequentemente difundida de que as noites na floresta tropical são
calmas, sem eventos intensos.
As simulações com o LES reproduziram adequadamente várias características
observadas no escoamento turbulento na interface vegetação-atmosfera da floresta amazônica
e também possibilitaram a melhor compreensão de algumas características da estrutura
mecânica da turbulência atmosférica e sua variabilidade horizontal e vertical, tais como: i)
altura em que as ECs mecânicas se organizem na forma de “rolos”; ii) variabilidade vertical
das fases de “intrusão” e “ejeção”das ECs, do fluxo de momento, das skewness, do
coeficiente de correlação, dentre outros.
Esta Tese é composta por quatro manuscritos científicos apresentados como capítulos.
Um deles já foi publicado, estando atualmente disponível na versão online. Os outros três
artigos foram submetidos, mas ainda estão em processo de revisão. O capítulo 1 refere-se às
questões da variabilidade da escala temporal das ECs encontradas nas séries temporais de
temperatura acima da Rebio-Jarú e à sua relação com o API. O capítulo 2 está relacionado às
questões do arrasto superficial na interface floresta-atmosfera e à possibilidade de obtenção de
relação geral para o perfil da velocidade do vento médio acima e dentro da copa florestal, que
leva em conta o valor do índice de área de folha e o API. No capítulo 3 analisou-se a estrutura
da turbulência atmosférica, baseado na existência de três diferentes regimes turbulentos
noturnos acima da floresta amazônica. Tais regimes foram classificados de acordo com
metodologia proposto por Sun et al (2012), sendo eles: regime 1) turbulência fraca e vento
fraco; regime 2) forte turbulência e velocidade do vento alta 3) eventos turbulentos
intermitentes. No capítulo 4 usou-se o modelo LES para simular o escoamento turbulento
acima da floresta amazônica. Para tanto, foi inserido no modelo uma força de arrasto,
representativa de um típico dossel florestal amazônico. Os resultados das simulações
5
mostraram-se sensíveis a presença do dossel com um nítido ponto de inflexão no perfil
vertical do vento.
Elementos Complementares.
Neste tópico irei mencionar algumas etapas importantes vividas por mim, durante o
período em que estive cursando o Doutorado em Clima e Ambiente:
 Participei do “São Paulo Spring School on Urban Climate at Tropical
Regions”, realizado na Universidade de São Paulo (USP), em setembro de 2013.
Neste evento apresentei o trabalho “vertical variability of the turbulent flow over
rough surfaces”, o qual foi escolhido o melhor trabalho apresentado no evento;
 Apresentei o trabalho “A Study of Distinct Turbulence Night-time
Regimes above Amazon forest in ATTO-Site” no workshop do ATTO, realizado
em abril de 2014 no instituto Max Planck, em Mainz/Alemanha;
 Fiz um estágio sanduíche, pelo Programa Ciência sem Fronteiras, sob
supervisão do pesquisador Mathhia Mauder no Karlsruhe Institute of
Technology (KIT), Institute of Meteorology and Climate Research Atmospheric
Environmental
Research
(IMK-IFU),
Campus
Alpin,
Garmisch-
Partenkirchen/Alemanha, durante os períodos de abril a julho de 2014;
 Também obtive resultados para o sítio experimental do Uatumã que
foram publicados no trabalho “Andrea et al. (2015) The Amazon Tall Tower
Observatory (ATTO) in the remote Amazon Basin: overview of first results
from ecosystem ecology, meteorology, trace gas, and aerosol measurements,
Atmos. Chem. Phys. Discuss., 15, 11599-11726, doi:10.5194/acpd-15-115992015”;
 Apresentei o trabalho “LES Applied to Analyze the Turbulent Flow
Organization
above
Amazon
Forest,”
no
GoAmazon2014/15
Conference, realizado em maio de 2015, na universidade de Harvard.
Science
6
OBJETIVO
Investigar, através de dados observacionais e modelagem numérica (LES), a variabilidade
vertical da estrutura da turbulência atmosférica na camada limite convectiva e noturna, acima
da floresta amazônica, sob diferentes condições de estabilidade atmosférica.
7
Capítulo 1
__________________________________________________
Dias-Junior, C.Q. Sá, L.D.A. Pachêco, V.B. de
Souza,
C.M.
2013.
Coherent
structures
detected in the unstable atmospheric surface
layer above the Amazon forest. Journal of
Wind
Engineering
Aerodynamics, 115:1-8.
and
Industrial
8
Coherent structures detected in the unstable atmospheric surface layer
above the Amazon Forest
C.Q. Dias-Juniora, L.D.A Sáb, V.B. Pachêcoc, C.M. de Souzaa.
a
b
Instituto Nacional de Pesquisas da Amazônia (INPA) , Av. André Araújo, nº 2936, Aleixo, Manaus,
Amazonas, Brazil
Centro Regional da Amazônia (CRA), Instituto Nacional de Pesquisas Espaciais (INPE), Parque de
Ciência e Tecnologia do Guamá, Av. Perimetral, nº 2651, Belém, Pará, Brazil,
c
Universidade Federal do Amazonas, Av. General Rodrigo Octávio, nº 6200, Coroado I, Manaus,
Amazonas, Brazil.
Abstract
Some characteristics of the turbulence structure above primary forest localized in the
south-western Amazon are analyzed. The data was collected in 60 m height meteorological
tower erected in Rebio- Jarú Reserve, Brazil. The Morlet’s wavelet is used to detect coherent
structures (CS) “ramp” time scales from turbulent virtual temperature data measured above
forest, under day-time conditions. It is shown that there is a close relationship between time
scale of the coherent structure (TCS) and the height to the inflection point in the mean wind
speed profile (IP). A time scale associated with the IP is used to provide useful information on
inside canopy penetration flow in order to be compared with the CS time-scale. The results
show a very robust correlation between these two time scales (for 144 half - hourly data sets,
a correlation coefficient value of 0.9 have been obtained). Such results provide new insights
regarding shear instability and turbulent eddy characteristics above tall vegetation, in the
surface roughness sub-layer (SRS).
Keywords: Turbulence; Coherent structures; Roughness sub-layer; Wind profile; Shear instability;
Time-Scales; Wavelets.
1. Introduction
The first investigations regarding atmospheric flow similarity relationships above
forest canopies have pointed out turbulent exchange above and below tall vegetation as scalar
diffusivity anomalies (Thom, 1975) and the existence of a roughness transition sub-layer
(RTS) associated with turbulent flow above very complex surfaces as forests and the failure
9
of the familiar Monin-Obukhov Similarity Theory (MOST) which is suitable for smooth and
horizontally homogeneous surfaces (Högström and Bergström, 1996; Raupach and Thom,
1981). In the RTS, turbulent exchange processes are strongly influenced by coherent
structures generated by shear instability mechanisms associated with the existence of the
inflection point in the mean wind profile. Actually strong wind shear in the forest-atmosphere
interface creates regions of peculiar coherent “roll” eddies (Gerz et al., 1994; Boldes et al.
2003; Boldes et al., 2007; Raupach et al., 1996; Robinson, 1991) and generates spectral shortcircuiting and wake production within the canopy trunk space (Cava and Katul, 2008;
Finnigan, 2000). Such features introduce new kind of problems in applying footprint and fetch
concepts for measuring meteorological variables (Horst and Weil, 1992; Lee, 2003), and in
estimating vertical fluxes (Horst and Weil, 1994; Mahrt, 2010; Sakai et al., 2001).
One important issue associated with the role of Amazonian forest in biosphereatmosphere exchanges, is the momentum transfer from the atmosphere to the surface.
Problems related to the coupling between above canopy flow and below Amazonian forest
canopy flow have been discussed by authors as Fitzjarrald et al., (1990), Kruijt et al., (2000),
Silva Dias (2002), Viswanadham et al., (1990), among others. Despite much work being
developed on this subject, there are few studies relating wind speed profile inflection point
occurrence and scalar ramp (CS) characteristics, as time or frequency scales (Raupach et al.,
1996; Thomas and Foken, 2005) above tall vegetation. CS are ubiquitous in turbulent flows
(Antonia, 1979; Boldes et al., 2007; Gilliam et al., 2000; Jordan et al., 1997; Thomas and
Foken, 2007). They are distinct large-scale fluctuation patterns regularly observed in turbulent
flows (Wilczak, 1984). Above tall forests CS are linked with inside canopy gust penetration,
and present specific frequency or time-scale of occurrence. Two time (or frequency) scales
are compared: the time of occurrence of CS based on Gao and Li (1993) procedure of
detecting TCS in a TV (virtual temperature) time-series using wavelet transform, and a time
scale related with a gust penetration scale, calculated using inflection point in the mean wind
speed profile information, as proposed by Marshall et al. (2002). The gust penetration time
scale proposition is based on Robinson (1991) discussion about the consequences of the
existence of an inflection point in the wind speed profile above tall vegetation which is
capable to generate slow-dissipation rolls-like CS, which are ranged transversally to the mean
stream flow. According to Raupach et al. (1996), and their “mixing layer analogy”, such CS
are related to the creation of an oscillation mode and vorticity generation at the interface
10
between above and inside canopy flows. It is just this kind of oscillation which is to be
detected. To this end analyses are carried out using the proposed time scale.
2. Experimental and methods
2.1. Site and data
The biological forest reserve of Jarú is a 268,000 hectares located in south-western
Amazon, (Andreae et al., 2002). It is an area of typical tropical rain forest, between 10005'S and
10019'S and between 61035'W and 61057'W, at approximately 145 m above sea level height. A
60 m height micrometeorological tower with the following coordinates 1004’42.36’’ S;
61056’1.62’’ W (Zeri and Sá, 2010) was built in the Rebio-Jarú Reserve (Fig. 1), which presents
homogeneous fetch conditions from north-west to south-east sides of the tower (in a clockwise
sense). At the remaining directions, around 1km homogeneous fetch conditions hold (Sá and
Pachêco, 2006). River Machado is approximately 800m at southern side. Culf et al. (1996)
present geographical and climatological information concerning this experimental site in which a
60m height meteorological tower has been erected. As mentioned by von Randow et al.
(2002), at the top of the tower, a vertical beam was placed in which a 3-D sonic anemometer
(CSAT3, Campbell Scientific Inc.), whose specifications are described in the document
http://s.campbellsci.com/documents/us/manuals/csat3.pdf (Appendix C), was installed at the
height of 67 m above the forest floor, at a sampling rate of 16 Hz. The sonic anemometer has
measured the three wind components (u,v,w) and the sonic virtual air temperature (Tv), and it
is shown in Fig. 3. According to Andreae et al. (2002) forest canopy height ranges from 30 m
to 35 m. Wright et al. (1996) reported a 4.6 value for leaf area index and McWilliam et al.
(1996) also present information concerning the tree species found in the Rebio-Jarú Reserve.
The Rebio-Jarú Reserve is one of the several sites in which the Large Scale BiosphereAtmosphere Experiment in Amazonia (LBA) was carried out (Silva Dias et al., 2002). In the
present study 144 fast response virtual temperature half-hourly data sets sampled at 16 Hz
have been used, and low response wind profile data sampled at 0.1 Hz, corresponding to daytime periods of the 1999 Julian days 41, 42, 43, 45, 46, 50. As a part of the Rebio-Jarú
Reserve scientific activities energy budget components, wind velocity, temperature, humidity
data was measured at several heights on a micrometeorological tower. To investigate the
relationship between TCS and the IP, data provided by nine cup anemometers (Low Power
A100L2, Vector Instruments Inc.) ranged in previously defined heights to give accurate
resolution information regarding the inflection point in the mean wind speed profile have been
11
used, as shown in Fig. 2. Thus, 1 hour averaged wind speed values, which have been
measured at heights of 55.00 m, 50.55 m, 47.70 m, 42.90 m, 40.25 m, 37.80 m, 32.8 m, 26.65
m, and 14.30 m above the ground, are available for calculations.
Virtual temperature time series has been obtained with sonic anemometerthermometer measurements. As the speed of sound varies with temperature and humidity, but
is approximately stable with pressure change, sonic anemometers are also used as
thermometers. Their basic principle is based upon the measurement of the traveling time of an
ultrasound pulse between two transducers. As is presented in the Manufacturer's Manual
(CSAT3 Three Dimensional Sonic Anemometer – Instruction Manual, Campbell Scientific,
Inc., 1998-2012, Appendix C), (http://s.campbellsci.com/documents/us/manuals/csat3.pdf),
the sonic virtual temperature, in degrees Celsius, is given by: Ts = (c2 / γd Rd) – 273. 15, where
γd = 1.4 is the ratio of specific heat of dry air at constant pressure to that at constant volume;
Rd = 287.04 J K-1 kg-1 is the gas constant for dry air; c is the sound velocity provided by the
sonic anemometer. It is important to remember that the effect of humidity on the speed of
sound has been included in the sonic virtual temperature Tv, Tv = Ts + 273.15 = T (1+ 0.61q),
where T is the air temperature and q is the air specific humidity.
Fig.1: Meteorological tower erected at Rebio-Jarú forest reserve.
12
Fig.2: Fast response instruments in the meteorological tower at Rebio-Jarú.
Fig. 3: Cup anemometers ranged at different heights in the meteorological tower at Rebio-Jarú
2.2. Meteorological conditions
Several environmental data of the Rebio-Jarú reserve in 1999, during the experimental
field campaign (from February 10th to March 08th 1999), are presented by Pachêco (2001) and
Table 1 presents some meteorological information such as maximum and minimum values of
the atmospheric pressure (to 30 m height), wind speed (to 55.00 m height) and air temperature
(to 54.90 m height) measured at the meteorological tower, during the experimental field
campaign.
13
Julian
days
Atmosp.
pressure (mb)
maximum
41
42
43
44
45
46
47
48
49
50
51
55
56
57
58
59
60
61
62
63
64
65
66
67
994.8
994.5
994.5
993.8
995.0
995.3
995.0
994.2
995.5
994.5
994.3
995.0
993.6
994.7
993.5
992.4
990.8
992.4
993.5
993.4
993.2
991.8
990.1
991.1
Atmosp.
pressure (mb)
minimum
988.2
988.0
987.9
987.8
987.7
988.3
988.2
987.8
989.5
989.5
989.0
990.1
987.0
987.5
987.6
986.2
985.0
987.8
989.2
986.0
986.8
985.9
984.5
985.9
Air
temp.(ºC)
maximum
30.8
30.5
33.2
32.2
32.5
30.6
30.4
30.5
29.4
30.7
29.1
26.4
29.2
28.6
28.3
28.7
30.1
28.5
30.3
30.6
29.4
29.7
30.2
28.3
Air
temp.(ºC)
minimum
Wind speed
(ms-1)
maximum
Wind speed
(ms-1)
minimum
2.80
2.95
2.91
3.60
3.72
3.75
2.65
3.14
3.02
4.31
3.55
3.16
3.61
4.36
2.81
3.72
3.83
3.54
3.62
4.37
4.76
3.18
3.25
3.01
0.83
0.62
0.61
1.15
0.88
0.96
0.51
0.87
0.82
0.58
0.79
0.65
0.88
0.96
0.69
0.51
1.57
0.64
0.71
0.64
0.64
0.57
0.58
0.91
23.2
24.4
23.3
24.3
23.6
23.4
23.9
24.2
22.7
23.6
23.1
22.5
23.1
23.1
23.2
23.8
23.4
22.4
23.7
22.8
23.7
22.9
23.0
24.2
Table I: Rebio-Jarú meteorological data obtained the 1999 experiment field campaign.
In the Fig. 4.a and 4.b is shown the mean wind direction. The first associated with the
day-time, at times when the convective activity generated by surface-heat is greater; there is a
clear predominance of northern winds. The second corresponds to the night-time and early
morning, there are two preferential directions for the wind: one continues to be of the north,
but the other corresponds to the opposite direction. It is possible that the prevalence of
southern winds in some periods is associated with the situation in which the wind speed is
weak such way to predominate effects linked to local experimental site topography.
Effectively, to the southeast of the tower, there were small hills tens of meters high and it is
possible that they induce the katabatic wind formation in the northern region. Moreover, the
Fig. 5 shows precipitation data, in mm, for each day of the experiment.
14
Fig. 4: Histogram of frequency of wind direction for observations of the intervals: (a) from 11:00 to
16:00 local-time and (b) from 20:00 up to 9:00 local-time.
Fig. 5: Total precipitation for Julian days: 41 to 51 and 55-67.
2.3. Data quality control
Before performing the statistical calculations with Rebio-Jarú reserve data, they have
been submitted to quality control tests. In a first step of this procedure, a visual inspection of
all available meteorological time-series has been performed. In situations in which this
procedure did not reveal itself sufficient, a data quality control based on Vickers and Mahrt
(1997) has been used. These authors have compiled several methods to assess the quality of
turbulent data, proposed by several authors and applied to data obtained at well-known
micrometeorological field campaigns such as RASEX, Microfronts95 and BOREAS with
satisfactory results.
2.4. Methods
Two kinds of meteorological information have been used in order to compare time
scale characteristics of the “ramp” coherent structures and the inflection point in the mean
wind speed profile:
15
i) Vertical mean profiles of the wind speed obtained from cup anemometer data. Based
on these profiles, third degree polynomial function fittings have been performed to determine
the inflection point height for each data run.
ii) Time series of virtual temperature to detect, the time-scale of coherent structures by
means of wavelet transform application as proposed by Gao and Li (1993) and explained as
follows.
To detect CS on a virtual temperature time series, sampled at 16 Hz rate, a continuous
one-dimensional wavelet transform (Eq.1) has been used, which is defined when applied to a
given signal f(t) as:
W f a, b  
1
a


-
t-b
f t   
 dt
 a 
(1)
Where a ∈ ℛ+ and b ∈ ℛ.
The wavelet is a mathematical function which has some special properties (Farge,
1992): i) Admissibility: The analyzing function has to have its average equal to zero; ii)
Similarity: The scale decomposition is carried out by translation and dilatation of one only
“mother wavelet”, is stretched or compressed and displaced along the time to generate a
family of “daughter wavelets”, which are expressed as function of two parameters: one for the
scales (a), and other for the time position (b). With the set of daughter wavelets, a time series
can be decomposed at different scales, and thus, it is possible to calculate by-scale statistical
relevant information (Furon et al., 2008).
Is used the Morlet’s complex function (Eq. 2) which is suitable for coherent structure time
scale analysis, as deeply discussed by Thomas and Foken (2005).
    

1
4
ei 0  e 
2
/2
(2)
where η is the dimensionless parameter of time and ω0 is the dimensionless frequency. Other
types of wavelet functions and their characteristics can be found at Torrence and Compo
(1997).
According with Gao and Li (1993), the scale of occurrence of CS in scalar data, such
as virtual temperature time-series, may be determined using the scale variance of wavelet
coefficients of the available data (Eq. 3). The TCS corresponds to the one in which the
wavelet coefficient variances reach its maximum value.
16
 a, b   T f a, b  db
2
(3)
where T f (a, b) is the Morlet’s Wavelet Transform.
As shown in Fig. 6, for a day-time half-hourly data set of Rebio-Jarú reserve (10
February 1999, 09:00 h – 09:30 h, local time), the largest variance corresponds to the time
scale of about 78 s. Thus, this value is considered as the TCS for virtual temperature “likeramp” structures above forest canopy.
Fig. 6: Scale variance of the wavelets coefficients as a function of the time scale, for virtual
temperature time series obtained from 09:00 h - 09:30 h, local time, 10 February , 1999.
To investigate the mechanical turbulent processes observed near the inflection point in
the mean wind speed profile, which are dominated by peculiar like-roll coherent structures
(Robinson, 1991), is proposed an IP time scale (ti), based on the vertical wind shear observed
in this region, which is defined as:
ti 
z
f
 zi 
u
f
 ui 
(4)
Where zf is the fixed height (67 m) in which the fast response turbulent data has been
recorded, zi is the inflection point height (which changes along the day), and uf and, ui are the
30 min wind speed mean values measured at zf and zi, respectively. Thus, it is a logical
assumption to suppose that ti value contains information concerning the inside canopy
penetration capability of a like-roll vortex, or in other words, that it contains some
information regarding the rate at which this vortex will be dissipated by the forest canopy.
17
To investigate wind mean profile characteristics and to calculate the inflection point
height in the mean wind speed profile, a third degree polynomial function least square
numerical best fit has been done. Once obtained the best fitted function, it was possible to
calculate the inflection point height (zi) as shown in the Fig. 7 (for this data set, a value of
38.36 m for the inflection point height has been found).
Fig. 7: Third degree polynomial best fitting for the vertical wind speed profile (low response wind
speed data measured from 15:30 h -16:00 h, on 19 February, 1999.
Pachêco (2001) calculated the profile of vertical of the dimensionless wind velocity
for three different conditions: clear sky, partially covered with sky cloud and overcast. His
adjustments polynomials of vertical profiles of wind velocity do not seem to have been
influenced by the sky coverage. In the Fig. 8 has been shown a dimensionless vertical wind
profile graph provided by Pachêco (2001) for conditions of partially covered sky, situation
frequently found in the Amazon. Yet, according to Pacheco (2001), the change of cloud
coverage does not generate significant changes in the wind velocity vertical profile.
18
Fig. 8: Vertical profile of dimensionless wind velocity for a partially overcast sky.
3. Results
To emphasize the similar shapes of the curves representing the along day-time
variation of the inflection point height, zi, and of the TCS, Fig. 9 and Fig. 10 are presented, for
data collected at the Rebio-Jarú forest reserve. It clearly shows that zi and TCS ranges from
along the day. After 7:00 h there is a decrease tendency in zi values from around 41 m to 38
m, which remains almost constant between 11:00 h and 13:30 h. After this time, zi displays a
slower but clear increase tendency up to 18:00 h, when it stabilizes around a 41 m height. On
the other hand, the TCS value has a slow decrease during the morning: from approximately 75
s at 06:00 h to 50 s at noon. After 13:00 h it depicts a slow increase during afternoon and
reaches a value of 75 s at 18:00 h. Regarding the data gathered above the forest, in spite of
some uncertainty in the data (concerning zi and TCS calculations) it is observed a close
relationship between the TCS and the height of the inflection point in the mean wind speed
profile above forest, zi.
The suggested assumption is that TCS variation is associated with a “roll-like” vertical
displacement in its location above the forest canopy. As reported by Raupach et al. (1996) and
Robinson (1991), such eddies, ranged transversally to the wind direction, dissipated kinetic
energy in a slower way (time scales of about 60 s) when compared to the turbulent eddies
generated above “smooth” surfaces (time scales of about 30 s), ranged along the wind
direction. The minimum TCS value corresponds to the minimum inflection-point height and
this should be associated to a more effective kinetic energy dissipation when the roll-like eddy
approximates of the top canopy region, with its roughness elements acting as wake generators,
increasing wind-shear effects and thus, the decreasing the TCS.
19
Fig. 9: Evolution of the coherent structures time-scale hourly-mean values (a) and the vertical wind
profile inflection point height (b), along with their standard deviations, obtained above Rebio-Jarú
forest reserve, for 144 available half-hourly data sets.
Fig. 10: Comparison of the evolution of the inflection point height and the coherent structures timescale above Rebio-Jarú forest reserve.
To search more quantitative information concerning the above relationship, a
numerical linear fit of the IP height value, zi, against the TCS has been done, as shown in Fig.
11.
20
Fig. 11: Comparison between the inflection point height and the coherent structure time-scale for 144
run data for day-time conditions.
Despite the narrow zi band variation (37 m to 42 m), the linear regression between
TCS and zi presented reasonable least square fit, with a correlation coefficient next to a 0.8
value, for 144 half-hourly data sets. This result reinforce the assumption concerning the
existence of a close relationship between two distinct turbulent parameters: a mechanical
variable, zi, associated with the mean wind speed vertical profile and a thermodynamic
variable, TCS, associated with virtual temperature coherent structures, whose time scale is
detectable by wavelet analysis.
To perform a comparison between inflection point into canopy penetration
characteristics and TCS on basis of a same physical fundamental dimension, information
provided by an IP time scale is used and expressed in Eq. 4, based on the assumption that it
contains physical information about the capability of penetration into canopy of a roll-like
vortex. A linear fit regression comparing the two investigated time scales is presented in Fig.
12.
21
Fig. 12: Comparison of two time-scales: coherent structure time scale (y-axis) and inflection point
time-scale (x-axis) for 144 half-hourly data sets.
The results seem to agree with Raupach et al. (1996) findings, in which they argue that
active turbulence and coherent motions near the top of a vegetation canopy are patterned on a
plane mixing layer as a consequence of instabilities associated with the existence of an
“inflection point in the mean wind speed profile”. As uttered by Raupach et al. (1996), such
“mixing-layer turbulence” analogy formed around an IP would be associated with the
existence of two co-flowing streams of distinct velocities, which differ in many ways from
classical atmospheric surface layer turbulent structure observed above gentle surfaces.
Regarding IP day-time variability assumption, the results corroborate Marshall et al. (2002)
findings concerning the choice of new appropriate turbulent scales for obtaining general
relationships for near tall vegetation atmospheric flow. The best linear fit comparison of these
two time scales (IP and CS) shown in the Fig. 12, has provided a correlation coefficient
remarkably good, (approximately 0.9 correlation coefficient for 144 half-hourly data sets) for
day-time period. Coherent structure patterns near forest canopy are related to at least two
phenomena: vertical wind shear stress near the top of canopy and scalar vertical gradient (Paw
U et al., 1992; Warhaft, 2000). Thus, mechanical processes such as role–like vortex might
influence near forest canopy ramp-like structures associated with virtual temperature time
series. Therefore, the dependence between the frequency of CS and the IP height and even the
IP time scales should be explained by this kind of relationship.
22
In effect, Bolzan and Vieira (2006) have studied some characteristics of atmospheric
turbulence on the same experimental site studied by us. They have used an approach of Katul
et al. (1995) based on the correlation coefficient calculation among different scales of the
turbulent flow and also based on the "cross wavelet power" (CWP) analysis.
Their study focused on interactions among turbulent time series of vertical wind
velocity, w, and temperature, T, suggested that scale correlations for the w data increase
considerably when thermal coherent structures are present. These are distinctly shaped "likeramps "corresponding to time intervals between approximately 1.7 and 3.7 min, which could
be related to vertical thermal gradients in the atmosphere. They would promote an increase in
the interaction between these variables, w and T, and also depend on the atmospheric stability
conditions.
They also found a characteristic scale for relations among scales, which is probably
associated with processes of coalescence of vortices in ABL, as discussed by McNaughton
(2004), and the movements in the larger scales of the atmospheric unstable flow show much
less coherence for wind field, compared to the thermal field (Belušić and Mahrt, 2012), what
reinforces the assumption of Bolzan and Vieira (2006) regarding the probable influence of
thermal factors in explaining their results. These authors show that it is clearly observed an
increase of correlation among w scales for a scale located around 34s, for both daytime and
the nighttime conditions.
It should be emphasized that the results of Bolzan and Vieira (2006) are not
necessarily in opposition to the results of this investigation (in which variations were found in
the range of occurrence of coherent structures detected in time series of T), since the
methodology used to detect coherent structures is different from that used by Katul et al.
(1995), which is based on correlation among scales.
A good explanation to support this assertion is based on the assumption Belušić and
Mahrt (2012), according to which the structure of the turbulent processes in the atmospheric
surface boundary layer (ASL) is such that, even when occurring physical processes that act to
change the turbulent structure turbulence with time, the relations among scales, surprisingly,
appears to remain the same, which led Belušić and Mahrt (2012) to raise the issue according
with which "the geometry can be more universal than physics" in atmospheric turbulent
processes close to the surface.
That is, the timescale of occurrence of coherent structure above the canopy can change
throughout the day, as also changes the height of the inflection point of the profile of average
23
wind speed. However, the ratios of occurrences between different eddies, should not change
significantly.
Campanharo et al. (2008) when using high resolution temperature time series of the in
Rebio-Jarú site in Amazon, have obtained very interesting conclusions regarding the chaotic
nature of the flow above the forest canopy, with relatively low correlation dimension (D2 =
3.50 ± 0.05) and with the largest Lyapunov exponent λ1 = 0.050 ± 0.002.
These properties, according to them, are related, not to the existence of atmospheric
turbulence per se, but the occurrence of coherent structures within the atmospheric surface
layer, just above the forest canopy. These would make the atmospheric turbulent flow
considerably more "deterministic", despite its expected complexity in the forest-atmosphere
interface, as highlighted by Belušić and Mahrt (2012).
They attributed this increasing of "order" in the flow, at least in part, to the occurrence
of the inflection point instability of the flow near the top of forest canopy (Raupach et al.
1996).
Chian et al. (2008) have also analyzed the turbulent data measured above the Rebio
Jarú site and applying two different nonlinear techniques (kurtosis and phase coherence
index) showed that there is a clear increase of the scalar-velocity similarity for the turbulence
within the forest canopy when compared to the turbulence above the forest canopy.
They have suggested that the intermittency of turbulence existing within and above the
forest canopy of the Amazon rainforest is generated by phase coherence due to nonlinear
wave-wave interactions.
These results are obtained for Rebio-Jarú forest reserve. More investigation have to be
performed in order to improve our knowledge about mixed-layer analogy processes and also
obtain more general information corresponding leading scales on the RTS above tall
vegetation canopies.
4. Conclusion
Turbulent coherent structures in the atmospheric flow above Rebio-Jarú forest reserve
have been studied. Wind speed slow response data is used to detect inflection point height in
vertical wind profile and also an inherent time-scale related to mechanical vortex in the
interface forest-atmosphere (and its capability to penetrate into the forest canopy). Fast
response virtual temperature time series is used in order to detect ramp-like structures and its
associated time-scale using wavelet transform. It is shown that there are statistically robust
relationships between the inflection point height in the mean wind speed profile and TCS
24
associated with virtual temperature time series, which both change along the day with
minimum values next to noon time. It has been proposed also a time scale associated with
vertical wind shear (TWS) above the inflection point height and its displacement into the
forest canopy. These two time scales, TCS and TWS, displayed a very well good correlation.
These results are important in order to improve the understanding regarding the roughness
transition sub-layer and have implication to amend the parameterization of the exchange
processes.
Acknowledgements
The authors would like to thank all people which directly or indirectly contributed to
the fulfillment of the 1999 LBA – Intensive wet Campaign, and the support of the university
in Ji-Paraná (UNIR), Instituto Brasileiro do Meio Ambiente e dos Recursos Naturais
Renováveis (IBAMA) and Instituto Nacional de Colonização e Reforma Agrária (INCRA).
This work was done under the LBA project framework, sponsered by the European Union,
NASA, and Brazilian Agencies as the Conselho Nacional de Pesquisa e Desenvolvimento
Tecnológico (CNPq) and the Fundação de Amparo à Pesquisa do Estado de São Paulo
(FAPESP, process 01/06908-7). Leonardo Sá is particularly grateful to CNPq for his research
grant (process 303.728/2010-8). We thank Augusto Cesar Oliveira Freire for help with the
language
References
Andreae, M.O., Artaxo, P., Brandão, C., Carswell, F.E., Ciccioli, P., Costa, A.L., Culf, A.D.,
Esteves, J.L., Gash, J.H.C., Grace, J., Kabat, P., Lelieveld, J., Malhi, Y., Manzi, A.O.,
Meixner, F.X., Nobre, A.D., Nobre, C., Ruivo, M.L.P., Silva Dias, M.A., Stefani, P.,
Valentini, R., von Jouanne, J., Waterloo, M.J., 2002. Biogeochemical cycling of carbon,
water, energy, trace gases, and aerosols in Amazonia: The LBA-EUSTACH
experiments. J. Geophys. Res. 33, 1-25.
Antonia, R.A., Chambers, A.J., Phong-Anant, D., Rajagopalan, S., 1979. Properties of spatial
temperature derivatives in the atmospheric surface layer. Boundary-Layer Meteorol. 1,
101-118.
Belušić, D., Mahrt, L., 2012. Is geometry more universal than physics in the atmospheric
boundary layer flow? J. Geophys. Res. 117, Doi: 10.1029/2011JD016987.
25
Boldes, U., Scarabino, A., Di Leo, J. M., Colman, J., Gravenhorst, G. 2003. Characteristics of
some organized structures in the turbulent wind above and within a spruce forest from
field measurements. J. Wind Eng. Ind. Aerodyn. 91, 1253-1269.
Boldes, U., Scarabino, A., Colman, J. 2007. About the three-dimensional behavior of the flow
within a forest under unstable conditions. J. Wind Eng. Ind. Aerodyn. 95, 91-112.
Bolzan, M.J.A., Vieira, P.C., 2006. Wavelet analysis of the wind velocity and temperature
variability in the Amazon forest. Braz. J. Physics, 36, 1217-1222.
Campanharo, A.S.L.O., Ramos, F.M., Macau, E.E.N., Rosa, R.R., Bolzan, M.J.A., Sá,
L.D.A., 2008. Searching chaos and coherent structures in the atmospheric turbulence
above amazon forest. Phil. Trans. R. Soc. A, 366, 579-589.
Cava, D., Katul, G.G., 2008. Spectral short-circuiting and wake production within the canopy
trunc space of an alpine hardwood forest. Boundary-Layer Meteorol. 126, 415-431.
Chian, A.C.-L., Miranda, R.A., Koga, D., Bolzan, M.J.A., Ramos, F.M., Rempel, E.L., 2008.
Analysis of phase coherence in fully developed atmospheric turbulence: Amazon forest
canopy. Nonlin. Processes Geophys. 15, 567-573.
Culf, A.D.,
Esteves,
J.L.,
Marques Filho, A.O., Rocha,
H.R.,
1996,
Radiation,
temperature and humidity over forest and pasture in Amazonia, In: Gash, J.H.C.,
Nobre, C.A., Roberts, J.M., Victoria, R.L. (Eds), Amazonian Deforestation
and
Climate. John Wiley, Chichester, pp. 175-191.
Farge, M., 1992. The wavelet transform and its applications to turbulence. Annu. Rev. Fluid
Mech. 24, 395-457.
Finnigan, J.J., 2000. Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519-571.
Fitzjarrald, D.R., Moore, K.E., Cabral, O.M.R., Scolar, J., Manzi, A.O., Sá, L.D.A., 1990.
Daytime turbulent exchange between the Amazon forest and the atmosphere. J.
Geophys. Res. 10, 16825-16838.
Furon, A.C., Wagner-Riddle, C., Smith, C.R., Warland, J.S., 2008. Wavelet analysis of
wintertime and spring thaw CO2 and N2O fluxes from agricultural fields. Agr. Forest
Meteorol. 148, 1305-1317.
Gao, W., Li, B.L., 1993., Wavelet analysis of coherent structures at the atmosphere-forest
interface. J. Appl. Meteorol. 32, 1717-1725.
Gerz, T., Howell, J., Mahrt, L., 1994. Vortex structures and microfronts. Phys. Fluids, 3,
1242-151.
Gilliam, X., Dunyak, J., Doggett, A. Smith, D. 2000. Coherent structure detection using
wavelet analysis in long time-series. J. Wind Eng. Ind. Aerod. 88, 183-195.
26
Högström, U., Bergström, H., 1996. Organized turbulence in the near-neutral atmospheric
surface layer. J. Atmos. Sci. 17, 2452-2464.
Horst, T.W., Weil, J.C., 1992. Footprint estimation for scalar flux measurements in the
atmospheric surface layer. Boundary-Layer Meteorol. 59, 279-292.
Horst, T.W., Weil, J.C., 1994. How far is far enough? The fetch requirements for
micrometeorological measurement of surface fluxes. J. Atmos. Ocean. Tech. 11, 10181025.
Jordan, D.A., Hajj, M.R., Tieleman, H.W. 1997. Characterization of turbulence scales in the
atmospheric surface layer with the continuous wavelet transform. J. Wind Eng. Ind.
Aerod. 69-71, 709-716.
Katul, G.G., Parlange, M.B., Albertson, J.D., Chu, C.R., 1995. Local Isotropy and Anisotropy
in the Sheared and Heated Atmospheric Surface Layer. Boundary-Layer Meteorol. 72,
123-148.
Kruijt, B., Malhi, Y., Lloyd, J., Nobre, A.D., Miranda, A.C., Pereira, M.G.P., Culf, A., Grace,
J., 2000. Turbulence statistics above and within two Amazon rain forest canopies.
Boundary-Layer Meteorol. 2, 297-331.
Lee, X., 2003. Fetch and footprint of turbulent fluxes over vegetative stands with elevated
sources. Boundary-Layer Meteorol. 107, 561-579.
Mahrt, L., 2010. Computing turbulent fluxes near the surface: Needed improvements. Agr.
Forest Meteorol. 150, 501-509.
Marshall, B.J., Wood, C.J., Gardiner, B.A., Belcher, B.E., 2002. Conditional sampling of
forest canopy gusts. Boundary-Layer Meteorol. 102, 225-251.
McNaughton, K.G., 2004. Turbulence structure of the unstable atmospheric surface layer and
transition to the outer layer. Boundary-Layer Meteorol. 112, 199-221.
McWilliam, A.L.C., Cabral, O.M.R., Gomes, B.M., Esteves, J.L., Roberts, J., 1996. Forest
and pasture leaf-gas exchange in south-east Amazonia. In: Gash J.H.C., Nobre C.A.,
Roberts J.M., Victoria R.L. (Eds.), Amazonia Deforestation and Climate. John Wiley,
Chichester, pp. 175-191.
Pachêco, V.B., 2001. Algumas Características do Acoplamento Entre o Escoamento Acima e
Dentro da Floresta Amazônica’. M.Sc Thesis, National Institute of Space Research, São
José dos Campos, Brazil, 98 pp. (in Portuguese).
Paw U, K.T., Brunet, Y., Collineau, S., Shaw, R.H., Maitani, T., Qiu, J., Hipps, L., 1992. On
coherent structures in turbulence above and within agricultural plant canopies. Agr.
Forest Meteorol. 61, 55-68.
27
Raupach M.R., Thom A.S. 1981. Turbulence in and above Plant Canopies. Annu. Rev. Fluid
Mech. 13: 97-129.
Raupach, M.R., Finnigan, J.J., Brunet, Y., 1996. Coherent eddies and turbulence in vegetation
canopies: The mixing-layer analogy. Boundary-Layer Meteorol. 78, 351-382.
Robinson, S.K., 1991. Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid
Mech. 23, 601-639.
Sá, L.D.A., Pachêco, V.B., 2006. Wind Velocity Above and Inside Amazonian Rain Forest in
Rondônia. Braz. J. Meteorol. 21, 50-58.
Sakai, R.K., Fitzjarrald, D.R., Moore, K.E., 2001. Importance of low-frequency contributions
to eddy fluxes observed over rough surfaces. J. Appl. Meteorol. 40, 2178-2192.
Silva Dias, M.A.F.S., Rutledge, S., Kabat, P., Silva Dias, P., Nobre, C., Fisch, G., Dolman,
H., Zipser, E., Garstang, M., Manzi, A., Fuentes, J., Rocha, H., Marengo, J., PlanaFattori, A., Sá, L.D.A., Avalá, R.C.S., Andreae, M., Artaxo, P., Gielow, R., Gatti, L.,
2002. Clouds and rain processes in a biosphere atmosphere interaction context in the
Amazon Region. J. Geophys. Res. 20, 1-46.
Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, In: Monteith,
J.L., (Eds), Vegetation and the Atmosphere. Academic Press, London, pp. 57-110.
Thomas, C., Foken, T., 2005. Detection of long-term coherent exchange over spruceforest
using wavelet analysis. Theor. Appl. Climatol. 80, 91-104.
Thomas, C., Foken, T., 2007. Flux contribution of coherent structures and its implications for
the exchange of energy and matter in a tall spruce canopy. Boundary-Layer Meteorol.
123, 317-337.
Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis. Bull. Am. Meteorol.
Soc. 79, 61–78.
Vickers, D., Mahrt, L., 1997. Quality control and flux sampling problems for tower and
aircraft data. J. Atmos. Ocean. Tech. 14, 512-526.
Viswanadham, Y., Molion, L.C.B., Manzi, A.O., Sá, L.D.A., Silva Filho, V.P., André, R.G.B.,
Nogueira, J.L.M., dos Santos, R.C., 1990. Micrometeorological Measurements in Amazon
Forest during GTE/ABLE-2A Mission. J. Geophys. Res. 95: 13669-13682.
von Randow, C., Sá, L.D.A., Prasad, G.S.S.D., Manzi, A.O., Arlino, P.R.A., Kruijt, B. 2002.
Scale Variability of Atmospheric Surface Layer Fluxes of Energy and Carbon over a
Tropical Rain Forest in Southwest Amazonia. I. Diurnal Conditions. J. Geophys. Res.
107, 8062-8072.
Warhaft, Z., 2000. Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203-240.
28
Wilczak, J.M., 1984. Large-scale eddies in the unstably stratified atmospheric surface layer.
Part I: Velocity and temperature structures. J. Atmos. Sci. 41, 3537-3550.
Wright, I.R., Nobre, C.A., Tomasella, J., Rocha, H.R., Roberts, J.M., Vertamatti, E., Culf,
A.D., Alvalá, R.C.S., Hodnett, M.G., Ubarana, V.N., 1996. Towards a GCM surface
parameterization of Amazonia, In: Gash, J.H.C., Nobre, C.A., Roberts, J.M., Victoria,
R.L. (Eds), Amazonian Deforestation and Climate. John Wiley, Chichester, pp. 473504.
Zeri, M., Sá, L.D.A., 2010. The impact of data gaps and quality control filtering on the
balances of energy and carbon for a Southwest Amazon forest. Agr. Forest Meteorol.
150, 1543-1552.
29
Capítulo 2
__________________________________________________
de Souza, C.M. Dias-Junior, C.Q. Tota, J. Sá,
L.D.A. 2015. An empirical-analytic model to
describe the vertical wind speed profile above
and
within
condicionalmente
amazon
para
Applications em 15/06/2015.
forest.
Aceito
Meteorological
30
An empirical-analytic model of the vertical wind speed profile
above and within an amazon forest site
Cledenilson Mendonça de Souzaa,b, Cléo Quaresma Dias-Júniorb,e, Júlio Tótac, Leonardo
Deane de Abreu Sád
a
b
Universidade Federal do Amazonas – UFAM/ICSEZ, Parintins, AM, Brasil
Instituto Nacional de Pesquisas da Amazônia- INPA/ CLIAMB , Manaus, AM, Brasil.
c
d
e
Universidade Federal do Oeste do Pará – UFOPA, Santarém, PA, Brasil
Instituto Nacional de Pesquisas Espaciais – INPE/ CRA, Belém, PA, Brasil.
Instituto Federal de Educação Ciência e Tecnologia do Pará- IFPA, Bragança, PA, Brasil.
______________________________________________________________________
Abstract
This paper considers mean wind velocity profiles measured on a 60 m high tower in the
Rebio-Jarú forest (10° 04.7′ S, 61° 52.0′ W), located in the Brazilian north-western state of
Rondônia. The data were collected during the wet season intensive campaign of the LBA (Large
Scale Biosphere-Atmosphere Experiment in Amazonia). Nine cup anemometers were vertically
placed to provide a good estimate of the inflection point height of the mean velocity wind profile.
̅ (𝑧), based on key
The resulting data were used to formulate a mean vertical wind speed profile, 𝑢
parameters such as the inflection point height and leaf area index. The modified hyperbolic
tangent function was used to provide a more flexible fit to the experimental data. An exponential
̅ (𝑧) function, so that it can assume the appropriate ‘s’ shape near the
term was also added to the 𝑢
ground. Thus, some parameters were incorporated into the analytical profile function to enable
more flexibility. The presented results demonstrate that the profile is a good fit to experimental
data measured above and within the Amazon forest canopy.
Keywords: Wind profile; Roughness sub-layer; Modified hyperbolic tangent function;
Inflectional point; Amazon forest; Turbulence.
1. Introduction
Previous investigations regarding the validity of the atmospheric flow’s similarity
relationships above tall forest canopies noted some anomalous aspects of turbulent exchanges at
the forest-atmosphere interface (Thom et al., 1975). This raised interesting questions concerning
31
a roughness sub-layer (RSL), which is present above very complex surfaces such as forests
(Raupach and Thom 1981; Cellier and Brunet, 1992; Finnigan, 2000). It is difficult to estimate
turbulent fluxes under such conditions (Sakai et al., 2001; Von Randow et al., 2002; Mahrt,
2010) and new similarity relationships are required (Raupach et al., 1996; Marshall et al., 2002;
Sá and Pachêco, 2006). One important feature associated with these discrepancies is the
existence of an inflection point in the mean wind profile. This generates a new kind of turbulent
instability in the atmospheric flow because of the strong wind shear in the forest/atmosphere
interface, which may create regions with ‘like-roll’ coherent vortices (Robinson, 1991; Raupach
et al., 1996). These vortices have peculiar spectral characteristics (Campanharo et al., 2008,
Dias-Júnior et al., 2013), which may generate specific local phenomena such as spectral shortcircuiting and turbulent wakes caused by the interaction of the canopy forest with the turbulent
flow (Finnigan, 2000; Cava and Katul, 2008).
These complex flow characteristics make it difficult to accurately estimate mean
turbulent variables in the RSL near tall vegetation like the Amazonian forest (Sakai et al., 2001).
Thus, it is important to determine the momentum transfer from the atmosphere to the surface
when considering the role of the Amazonian forest in biosphere-atmosphere exchanges.
Problems related to the coupling between the atmospheric flow above and below the Amazon
forest canopy were studied by Fitzjarrald et al. (1990), Viswanadham et al. (1990), Kruijt et al.
(2000), Sá and Pachêco (2006) and Zeri et al. (2013), among others. Despite this extensive
research, there are few systematic studies that associated wind profile shapes with features of the
Amazon forest canopy (such as foliage structure), as investigated by Yi (2008) for a forest in a
temperate zone. These issues must be considered when developing surface-atmosphere exchange
schemes for modelling purposes, which is the focus of this paper.
2. Material and methods
2.1.
Experimental site
The Rebio-Jarú forest reserve is located in the southwestern Amazon. It is 2680 km2 of
typical tropical rain forest, and is located between 10° 05' S and 10° 19' S, and 61° 35' W and 61°
57' W, approximately 100–150 m above sea level (Zeri and Sa, 2010). A 60 m height
micrometeorological tower was built in the Rebio-Jarú reserve (Figure 1). According to Andreae
et al. (2002), it ‘presents horizontally homogeneous conditions from northwest to southeast,
which is the dominant wind direction (in a clockwise sense)’. Mc William et al. (1996) presented
information concerning the tree species found in this reserve. Culf et al. (1996), Andreae et al.
32
(2002) and Dias-Júnior et al. (2013) presented several geographical and climatic reviews of this
experimental site.
Several studies have considered the leaf area index (LAI) of Amazon forests, to estimate
its value in different Amazonia experimental sites. Among them, Moura (2001) proposed an
LAI of 6 for the Rebio-Jarú reserve, and Marques Filho et al. (2005) found LAI values of 6.4
and 6.1 for the ZF2 at km 14 and km 34 experimental sites, respectively. These sites are both
located next to Manaus, in the central Amazon. Roberts et al. (1996) used different methods
for estimating the LAI, and calculated values between 4.6 and 6 for the Rebio-Jarú reserve.
Based on this result, this study used a LAI value of 6.
Figure 1. Micrometeorological tower built on the Jarú Reserve.
Some investigations suggest that there may be a relationship between the vertical wind
̅ (𝑧)/𝑢
̅̅̅ℎ , is function of
profile and foliage structure. The findings of Yi (2008) imply that 𝑢
̅ (𝑧) is the mean wind vertical profile and ̅̅̅
LAI, where 𝑢
𝑢ℎ is the mean wind speed at the top of
the canopy. Doughty and Goulden (2008) analysed in situ and satellite data of the Tapajós
National Forest in the Amazon, approximately 150 km south of Santarém, Pará, Brazil. Their
results showed that the LAI was subject to seasonal variations. According to these
researchers, the LAI has a minimum value just over 4 m2 m−2 from December through to
April, a period that mostly corresponds to the local wet season. However, according to
Doughty and Goulden (2008), leaf production increases from July to September,
corresponding to the local dry season. During this period, many trees ‘change their old leaves
for new leaves’, and the LAI may reach 6 m2 m−2.
33
2.2.
Dataset
The Rebio-Jarú reserve is one of several experimental sites in the LBA (Large Scale
Biosphere-Atmosphere Experiment in Amazonia). The extensive LBA experimental campaigns
were carried out in two steps: The wet season campaign, from 25 January to 5 March 1999, and
the dry-to-wet campaign, from 15 September to 10 November 2002 (Silva Dias et al., 2002). As
a part of the scientific activities in the Rebio-Jarú reserve, the energy budget components, wind
velocity, temperature, and humidity were measured at several heights on a micrometeorological
tower. Nine cup anemometers (Low Power A100L2, Vector Instruments Inc.) sampled at 0.1 Hz
provided data for the wind profile, as shown in Figure 2. They were placed at previously defined
levels to provide accurate information about the inflection point height, and useful information
about the atmospheric flow in the forest-atmosphere interface. Thus, the instruments were
vertically installed at heights of 55.00 m, 50.55 m, 47.70 m, 42.90 m, 40.25 m, 37.80 m, 32.85
m, 26.65 m and 14.30 m.
We applied some of Vickers and Mahrt’s (1997) procedures regarding quality control of
the experimental data, to remove spurious spikes, amplitude resolution problems, dropouts and
unrealistic data.
Figure 2. Profile of the nine anemometers installed in the Jarú Reserve micrometeorological tower.
2.3.
Theoretical elements and methodology
There is some experimental evidence that similarity relationships based on Monin–
Obukhov similarity theory (MOST) cannot appropriately describe the atmospheric flow in the
RSL above tall vegetation (Thom et al., 1975; Cellier and Brunet, 1992; Raupach et al., 1996;
Finnigan, 2000; Py et al., 2004). Many empirical formulations for normalized 𝑢̅ (𝑧) in the RSL
have been proposed, based on roughness parameters distinct of the well-known zero-plane
34
displacement height (𝑑) and roughness length (𝑧0 ). Such relationships can more appropriately
express some exchange processes between the biosphere and atmosphere that occur near the top
of a tall forest (Raupach et al., 1996; Finnigan, 2000; Marshall et al., 2002; Py et al., 2004; Sá
and Pachêco, 2006; Doughty and Goulden, 2008; Tóta et al., 2012; Dias-Júnior et al., 2013).
Regarding some important issues associated with the wind profile’s shape above tall
vegetation in the RSL.
i) Fitzjarrald et al. (1990) obtained some evidence that suggests that the flow in the canopy
top provides information regarding a characteristic length scale (𝐿ℎ ) for the flow at the interface
between forest and atmosphere. That is,
̅
𝑢
𝐿ℎ = 𝑑𝑢̅ℎ ,
(1)
|
𝑑𝑧 ℎ
where 𝑢̅ℎ is the mean wind velocity at level ℎ (which corresponds to the mean canopy height)
̅
𝑑𝑢
and 𝑑𝑧 | is the mean velocity gradient at ℎ.
ℎ
ii) Raupach et al. (1996) used 𝐿ℎ to obtain a universal relationship that describes 𝑢̅(𝑧)
using the hyperbolic tangent function (HTF):
̅(𝑧)
𝑢
̅ℎ
𝑢
𝑧
= 1 + tanh (𝐿 ).
ℎ
(2)
iii) Marshall et al. (2002) used wind tunnel data, and Sá and Pachêco (2006) used
̅ (𝑧) that incorporates
experimental data from the Amazon forest to investigate a formulation for 𝑢
dynamical information of the inflection point height (𝑧𝑖 ) and the wind shear measured at ℎ. They
used scaling parameters: 𝑢𝑖 (mean wind velocity at 𝑧𝑖 ) as a characteristic velocity scale, and 𝐿ℎ
as defined in Equation (1). Their analyses were extended to both flows, above and within the
canopy. With these two characteristic scales, they obtained a general relationship for the vertical
profile:
𝑢̅⁄𝑢𝑖 = 𝐹[(𝑧 − 𝑧𝑖 )⁄𝐿ℎ ],
(3)
̅ is the mean wind velocity at 𝑧, and 𝐹 is a function whose mathematical form is
where 𝑢
determined empirically from experimental data. This fits very well with experimental data
measured far above the ground, but does not explain the influence of the canopy’s foliage
structure on the shape of the wind profile. To overcome this drawback, a new modified HTF
formulation was proposed, which was based on earlier models of vertical profiles in the RSL
35
̅ (𝑧) function to
(Raupach et al., 1996; Yi, 2008). A mathematical device was added to the 𝑢
obtain a better fit for this curve.
The theoretical bases for this proposition were presented by Raupach et al. (1996), who
considered an inflection point on the wind vertical profile next to the top of the canopy. They
suggested that the HTF can provide a good numerical fit to the wind’s vertical profile data.
However, a simple HTF cannot generate a good numerical fit, if the actual empirical function for
̅ (𝑧) is not exactly symmetrical with respect to 𝑧𝑖 . Thus, we propose a modified form of the HTF
𝑢
̅ (𝑧), which can more flexibly incorporate asymmetric shapes. Our
to improve the fit of 𝑢
technique can provide: 1) a good analytical model for the wind speed profile, which results in a
̅ (𝑧), which
good experimental fit for regions above and below 𝑧𝑖 ; and 2) a new formulation for 𝑢
incorporates some features of the vertical structure of the forest canopy and some aerodynamic
characteristics of the coupling between the flows above and within the canopy. The best fittingcurve is not perfectly anti-symmetric with respect to the horizontal axis at 𝑧𝑖 . Therefore, to
improve this fit, we inserted some flexible features into the best-fitting curve, making it less
rigid than the original HTF. For this, we propose a new argument for the HTF. Following on
from the HTF model formulations of Raupach et al. (1996) and Yi (2008), this leads to a new
̅ (𝑧) above and within the forest canopy:
formulation for 𝑢
𝑢̅(𝑧) = ̅̅̅̅
𝑢𝐻 {𝑡𝑎𝑛ℎ [𝛽 + 𝛾𝑒𝑥𝑝 (−𝐿𝐴𝐼(1 − 𝑧⁄𝑧𝑖 ))]},
(4)
where H is the height of the highest measuring level (55 m, for the Rebio-Jarú experimental
site); ̅̅̅̅
𝑢𝐻 is the mean wind speed at the 𝐻; 𝛽 and 𝛾 are fitting parameters; 𝑧𝑖 is the inflection
̅ (𝑧) is the mean wind
point height of the vertical wind profile; 𝑧 is a measuring height; and 𝑢
speed at z. 𝛽 and 𝛾 are new parameters, which are explained as follows.
𝛽 influences the lower wind profile. That is, it can change the wind profile within the
forest canopy. This is mainly useful for wind profiles in regions where there is a secondary
maximum in the wind profile, due to the trunk spaces of forests (Kaimal and Finnigan, 1994,
pp. 77–79). In Amazon forests, such occurrences of secondary maximums in the wind profiles
can exist in forests located in slopes or valleys. For example, the forests studied by Araújo et
al. (2010) and Tóta et al. (2012) in their investigations regarding the effects of terrain
heterogeneity on atmospheric flows within tall vegetation. The 𝛽 parameter provides a bet fit
to the wind profile in these situations.
𝛾 influences the wind profile in the opposite way to β, that is, it amplifies the upper
part of the wind profile without introducing substantial changes to the lower part. The 𝛾
36
parameter can describe the wind profile’s shape over forests located in horizontally
homogeneous, smooth areas, where we do not expect drainage flows or secondary maxima. In
these situations, the forests’ LAI are sufficiently high to hamper momentum transport deep
into the canopy.
To improve the profile fit, and to allow for an ‘s’ shape near the ground (as suggested
̅ (𝑧). That is,
by Yi (2008)), we included an exponential term in the analytical form of 𝑢
𝑢̅(𝑧) = 𝑢̅𝐻 {[
−1+exp(𝜇𝑧)
exp(𝜔𝑧)
𝑧
] 𝛼𝑡𝑎𝑛ℎ [𝛽 + 𝛾 ∙ 𝑒𝑥𝑝 (−𝐿𝐴𝐼 (1 − 𝑧 ))]},
𝑖
(5)
where µ, 𝛼, 𝛽 , 𝛾, and 𝜔 are fit parameters and LAI=6 for the Rebio-Jarú forest (Moura, 2001).
𝛼, 𝜇, and 𝜔 are new parameters, and are described as follows.
𝛼 multiplies the entire second part of Equation (5), which describes the dimensionless
vertical profile of the wind speed above and within the forest canopy. Thus, it should produce
a better fit to the vertical wind profile, covering situations ranging from very light winds to
strong winds. In summary, 𝛼 is strongly correlated with the average wind speed at any time.
𝜇 and 𝜔 enable more flexibility in terms of the s-shaped region located below 𝑧=20 m.
̅ (𝑧). Thus, these parameters may
They do not influence the 𝑧𝑖 value on the superior part of 𝑢
incorporate some of the mechanical effects of the vegetation roughness and buoyancy effects.
They are intended to make 𝑧 dimensionless within the two arguments of the exponential
functions in Equation 5 (but not in Equation (4)). They are generally close to unity (i.e., 1).
However, the arguments are within the exponential functions, so they can introduce
considerable variations in the dimensionless wind profile. These parameters may be
considered as a single constant in this study. Note that in the Rebio-Jarú tower, the wind
velocities were recorded down to 𝑧=14 m.
3. Results
The first numerical experiment analysed the wind speed profiles provided by Equation
(4). The curves generated by this model and by experimental data are presented in Figure 3.
They depict shapes that are not fully symmetric with respect to the inflection point. Note that
the variables in Figure 3 are not dimensionless. Thus, this model was not built with the aim of
obtaining universal relationships, but simply to show the mean shape of the wind field under a
wide range of environmental conditions.
37
Figure 3. The observed vertical mean wind profile compared with the one provided by the Hyperbolic
model (Julian day 46; from 0800 a.m. to 0900 a.m.).
The 𝛽 and 𝛾 parameters in Equation (4) are linked to physical effects acting on and
above the inflectional point zone. These parameters are associated with the existence of a
roughness sublayer (Finnigan, 2000), its heterogeneous features resulting from the effect of
distinct canopy architectures on the turbulence structure (Baldocchi and Meyers (1988), and
its prevailing atmospheric stability conditions (Mahrt et al., 2001).
Figures 4 and 5 help to explain the physical meanings of 𝛽 and 𝛾. Figure 4 shows that
variations in 𝛽 change the inferior part of the curve representing the lower canopy region. In
contrast, Figure 5 shows how variations in 𝛾 change the behaviour of the curve in the region
near the canopy.
Figure 4. Modeled wind profiles for different values of the (β) parameter.
38
Figure 5. Modeled wind profiles for different values of the (γ) parameter.
Dias-Júnior et al. (2013) recently found that the 𝑧𝑖 values observed above the RebioJarú reserve varied over the day-time period. They found that 𝑧𝑖 tends towards a maximum
value of 41 m in the early morning and late afternoon. However, at noon, it falls to
approximately 38 m, as shown in Figure 6.
̅ (𝑧). Thus,
These 𝑧𝑖 values were used to test how well the modified HTF model fits 𝑢
̅ (𝑧) in Equation (4) was used to calculate the hourly wind profile data for 13
the function for 𝑢
February 1999 under two conditions: i) 𝑧𝑖 varied according to the Dias-Júnior procedure; and
ii) fixed 𝑧𝑖 .
̅ (𝑧) were obtained when: 1) 𝛽 had a fixed
These results indicate that the best fits for 𝑢
value of 0.13 (which was obtained after many empirical tests); and 2) 𝑧𝑖 and 𝛾 varied over the
̅ (𝑧). Physically, it expresses the
daytime period. 𝑧𝑖 incorporates the asymmetrical effect in 𝑢
influence of the canopy top forcing on a vortex centred on 𝑧𝑖 . (Raupach et al., 1996). In
contrast, 𝛾 has a similar daytime trend to 𝑧𝑖 , as shown in Figure 6.
39
Figure 6. Daytime hourly variation of inflection point height (solid line) and gamma values (dashed
line) for the Rebio-Jarú reserve.
̅ (𝑧), data from 13 February 1999
To compare the observed and modelled profiles, i.e., 𝑢
was used to calculate the correlation coefficients for each 𝑧. These were then used to estimate
a mean correlation coefficient, 𝑟 (Table 1). The results were calculated for two conditions, to
investigate variations to the wind profile shape over the daytime period. In condition 𝑟1 , the
values of 𝑧𝑖 varied; and in 𝑟2 the values of 𝑧𝑖 are held fixed (= 41 m). It is observed that 𝑟1 > 𝑟2 ,
an indication that the wind speed profile was better modeled for the situations in which 𝑧𝑖 was
considered as being a variable parameter.
Table 1. Day-time hourly variation of the parameters γ, r1 and r2 measured in the Rebio-Jarú reserve
for the Julian day 44, year 1999.
Hour
06:00
07:00
08:00
09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
r1
(zi variable)
0.989
0.986
0.996
0.989
0.983
0.983
0.983
0.987
0.990
0.986
0.989
0.991
r2
(zi = 41 m)
0.989
0.985
0.993
0.976
0.971
0.961
0.957
0.967
0.973
0.976
0.981
0.990
40
To investigate the physical role of each of these fit parameters, Figure 7 contains plots
̅ (𝑧) versus z, where only one parameter was varied in each subplot. Figure 7a shows the
of 𝑢
wind profiles for different values of α. It amplifies the wind speed values as a whole. Figure
7b shows the wind profiles for different values of β. These profiles have the same wind speed
value at the highest measurement. The differences between the two groups of wind profiles
are more pronounced in the region corresponding to the within canopy zone. Figure 7c shows
wind profiles for different values of γ. There is same split in wind speed values as in Figure
7b. However, unlike the previous figure, this split is more pronounced in the higher part of the
profile. Figure 7d presents wind profiles for different values of µ. The wind profile shapes in
Figure 7a and d are quite similar, except in the region immediately above the ground, where
the profiles in Figure 7d slowly converge to the same curve (unlike in Figure 7a). The wind
profile is very sensitive to changes in ω. Small variations can generate significant distortions
in the wind profile, as shown in Figure 7e. The LAI parameter has a marked influence on the
wind profile shape. When LAI is relatively small, the wind profile loses its s shape, as shown
in Figure 7f.
Figure 7. Modelled wind profiles for different parameter values: a) alpha; b) beta; c) gamma; d) mu;
e) omega; and e) LAI
According to Doughty and Goulden (2008), the information provided by Equation (4) and
the seasonal variability of LAI suggest that the vertical wind profile also undergoes seasonal
changes. This can be seen in Figure 8, which contains two modelled profiles generated using
̅ (𝑧) function, one for LAI=4.2 and the other for LAI=5.8. In this figure ̅̅̅
the 𝑢
𝑢ℎ =2.2 m s−1,
𝛽=0.25, 𝛾=0.5 and 𝑧𝑖 =39 m. These values are similar to those found by Doughty and Goulden
41
(2008) for the minimum and maximum LAI in the Amazon forest. Figure 8 shows the
differences between the 𝜕𝑢̅/𝜕𝑧 values at level 𝑧𝑖 for the curves representing dry and wet
periods. In the wet period, 𝜕𝑢̅/𝜕𝑧 in the region immediately above the canopy is greater than
during the dry season. Consequently, it is more difficult for the atmospheric flow to transfer
momentum into the canopy during the wet season than during the dry season, as expected.
Figure 8. Modelled wind profiles for two different values of LAI (4.2: dashed grey line and 5.8: black
solid line), which correspond to the seasonal extreme values in the Amazon forest.
There is another indication of a possible seasonal LAI variability in the Amazon
forest, and of its consequences concerning the surface drag imposed by the plant canopy on
the immediately above atmospheric flow. Mafra (2014) analysed the seasonal variability of
nocturnal turbulent regimes above the Amazon forest in the Uatumã experimental site (central
Amazon), using the methodology proposed by Sun et al. (2012). She found different values
for the threshold value (𝑉𝐿 ) of the average wind speed above the forest canopy that separates
the weak and strong turbulence regimes. Note that the physical processes behind this
threshold have recently received much attention (Martins et al., 2013; Mafra, 2014; Andreae
et al., 2015), and the associated physical transition process was designated as a ‘HOST‘
(hockey-stick transition) by Sun et al. (2015).
The 𝛽 and 𝛾 parameters inside the HTF argument are linked to physical effects, which
occur at the inflection point zone and above. They are probably associated to the existence of
the roughness sublayer, and the so called ‘mixing-layer analogy’ (Raupach et al., 1996),
which states that the wind speed profile above tall vegetation has an inflection point. This
suggests that the region separates into two flow layers with distinct velocities, in which we
expect a turbulent vortex, or, in the words of Cava and Katul (2008), a ‘dominant eddy’. This
42
vortex could also be associated with the organization of ‘rolls‘ in the atmospheric flow with
respect to rotation axes transverse to the mean stream direction (Robinson, 1991). However,
according to Dias-Júnior et al. (2013), the height of the wind profile inflection point varies
throughout the day. During the night, when the wind speed is sufficiently strong above the
Rebio-Jarú, 𝑧𝑖 increases creating conditions that allow the dominant eddy to penetrate more
strongly and deeply into the canopy (higher torque associated with the vortex). This generates
a more effective exchange of energy and mass between the regions above and within the
forest canopy (Dias-Júnior et al., 2015). At night, this process is associated with situations
where the average wind speed exceeds the threshold value (𝑉𝐿 ) for a ‘HOST‘ phenomenon
(Sun et al., 2015). This increases the effectiveness of the mixture in the forest-atmosphere
interface, challenging the traditional flux-profile relationships of HOST (Sun et al., 2015).
Figure 9 shows an abstract generalization of Figure 3, incorporating the features of a
hypothetical secondary maximum in the wind profile. This secondary maximum is sometimes
found in the trunk spaces of forests (Baldocchi and Meyers, 1988; Kaimal and Finnigan,
1994, pp. 77–79). Thus, the lower part of Figure 9 refers to a hypothetical analytical form for
̅ (𝑧)/𝑢
̅̅̅ℎ(z) near the forest floor. This, when incorporated into Equation (4) (the
the function 𝑢
HTF) results in Equation (5) (the so called ‘modified HTF’). Figure 9 shows that the mean
wind speed profile fits very well with the data.
Figure 9. Observed mean wind profile and associated standard deviation compared with hyperbolic
tangent function fitted data (second version).
43
4. Conclusions
This paper proposes an empirical-analytic model for describing the vertical wind
speed profile above and within an Amazon forest, and provides a general non-dimensional
relationship. The HTF was modified to obtain a better fit to experimental data collected above
and within the Amazon forest. This function provides a good fit in many experimental
situations, where there is variation in the height of the inflection point of the wind speed’s
vertical profile. These results are mainly useful for two reasons. First, they can be used to
obtain a realistic estimate of the vertical wind profile when there is a limited amount of data.
Second, they provide useful information regarding modifications to the wind profile shape,
which were introduced by several distinct conditions. These include changes to the LAI
values and changes to the height of the vertical profile’s inflectional point. This formulation
provides a better fit to the experimental data measured above and within the Amazon forest
canopy.
Acknowledgments
The authors would like to thank all people which directly or indirectly contributed to
the fulfillment of the1999 LBA - Intensive wet Campaign, and the support of the university in
Ji-Paraná (UNIR), Instituto Brasileiro do Meio Ambiente e dos Recursos Naturais Renováveis
(IBAMA) and Instituto Nacional de Colonização e Reforma Agrária (INCRA). This work was
done under the LBA project framework, sponsored by the European Union, NASA, and
Brazilian Agencies as the Conselho Nacional de Pesquisa e Desenvolvimento Tecnológico
(CNPq) and the Fundação de Amparo a Pesquisa do Estado de São Paulo (FAPESP, process
01/06908-7). Leonardo Sá is particularly grateful to CNPq for his research grant
(process303.728/2010-8).
References
Andreae MO et al. 2015. The Amazon Tall Tower Observation (ATTO): Overview of pilot
measurements on ecosystem ecology, meteorology, trace gases, and aerosols.
Atmospheric Chemistry and Physics Discussions. 15: 11599-11726.
Andreae MO, Artaxo P, Brandão C, Carswell FE, Ciccioli P, Costa AL, Culf AD, Esteves JL,
Gash JHC, Grace J, Kabat P, Lelieveld J, Malhi Y, Manzi AO, Meixner FX, Nobre AD,
Nobre C, Ruivo MLP, Silva Dias MA, Stefani P , Valentini R, von Jouanne J, Waterloo
44
MJ. 2002. Biogeochemical cycling of carbon, water, energy, trace gases, and aerosols in
Amazonia: the LBA-EUSTACH experiments. J. Geophys. Res. 33: 1–25.
Araújo AC, Dolman AJ, Waterloo MJ, Gash JHC, Kruijt B, Zanchi FB, Lange JME,
Stoevelaar R, Manzi AO, Nobre AD, Lootens RN, Backer J. 2010. The spatial
variability of CO2 storage and the interpretation of eddy covariance fluxes in central
Amazonia. Agric. For. Meteorol. 150: 226-237.
Baldocchi, DD, Meyers TP. 1988. Turbulence structure in a deciduous forest. BoundaryLayer Meteorol. 43(4): 345-364.
Campanharo ASLO, Ramos FM, Macau EEN, Rosa RR, Bolzan MJA, Sa LDA. 2008.
Searching chaos and coherent structures in the atmospheric turbulence above Amazon
forest. Phil. Trans. R. Soc. A 366: 579–589.
Cava D, Katul GG. 2008. Spectral Short-circuiting and Wake Production within the Canopy
Trunc Space of an Alpine Hardwood Forest. Boundary-Layer Meteorol. 126: 415-431.
Cellier P, Brunet Y. 1992. Flux-gradient relationships above tall plant canopies. Agric. For.
Meteorol. 58: 93-117.
Culf AD, Esteves JL, Marques Filho AO, Rocha, HR. 1996. Radiation, temperature and
humidity over forest and pasture in Amazonia. In Amazonian Deforestation and
Climate. Gash JHC, Nobre CA, Roberts JM and Victoria RL. Eds., Wiley, 175-191,
Chichester.
Dias Júnior CQ, Sá LDA, Pachêco VB, Souza CM. 2013. Coherent structures detected in the
unstable atmospheric surface layer above the Amazon Forest. J. Wind Eng. Ind.
Aerodyn. 115: 1–8
Doughty CE, Goulden ML. 2008. Seasonal patterns of tropical forest leaf area index and CO2
exchange. J. Geophys. Res. 113: G00B06.
Finnigan JJ. 2000. Turbulence in plant canopies. Ann. Rev. Fluid Mec. 32: 519-571.
Fitzjarrald DR, Moore KE, Cabral OMR, Scolar J, Manzi AO, Sá LDA. 1990. Daytime
Turbulent Exchange Between the Amazon Forest and the Atmosphere. J. Geophys. Res.
95: 16825-16838.
Kaimal JC, Finnigan JJ. 1994. Atmospheric Boundary Layer Flows. Their Structure and
Measurement. Oxford University Press, New York, 289 pp.
Kruijt B, Malhi Y, Lloyd J, Norbre AD, Miranda AC, Pereira MGP, Culf A, Grace J. 2000.
Turbulence Statistics Above and Within Two Amazon Rain Forest Canopies. BoundaryLayer Meteorol. 94: 297-331.
45
Mafra ACB. 2014. Características das trocas turbulentas noturnas de CO2 entre a floresta de
Uatumã, Amazonas, e a atmosfera. Dissertação de Mestrado em Ciências Ambientais,
Universidade Federal do Pará, Belém, Pará.
Mahrt L, Vickers D, Sun J, Jensen NO, Jorgensen H, Pardyjak E, Fernando H. 2001.
Determination of the Surface Drag Coefficient. Boundary-Layer Meteorol. 99: 249-276
Mahrt L. 2010. Computing turbulent fluxes near the surface: Needed improvements. Agric.
For. Meteorol. 150: 501-509.
Marques Filho AO, Dallarosa RG, Pachêco, VB. 2005. Radiação solar e distribuição vertical
de área foliar em floresta – Reserva Biológica do Cuieiras – ZF2, Manaus, Acta
Amazonica, 35(4): 427-436.
Marshall BJ, Wood CJ, Gardiner BA, Belcher BE. 2002. Conditional Sampling of Forest
Canopy Gusts. Boundary-Layer Meteorol 102: 225-251.
Martins HS, Sá LDA, Moraes OLL. 2013. Low level jets in the Pantanal wetland nocturnal
boundary layer – Case studies. American Journal of Environmental Energy, 3(1): 32-47.
Mc William ALC, Cabral OMR, Gomes BM, Esteves JL, Roberts JM. 1996. Forest and
pasture leaf-gas exchange in south-west Amazonia. In Amazonian Deforestation and
Climate. Gash JHC, Nobre CA, Roberts JM and Victoria RL Eds., Wiley, 265-285.
Moura RG. 2001. A study of the solar and terrestrial radiation above and inside a tropical rain
forest. MSc thesis in Meteorology, National Institute of Space Research, Brazil (INPE14015-TDI/1194).
Py C, de Langre E, Moulia B. 2004. The mixing layer instability of wind over a flexible crop
canopy. Comptes Rendus Mecanique, 332: 613-618.
Raupach MR, Finnigan JJ, Brunet Y. 1996. Coherent Eddies and Turbulence in Vegetation
Canopies: The Mixing-layer Analogy. Boundary-Layer Meteorol. 78: 351-382.
Raupach MR, Thom AS. 1981. Turbulence in and above Plant Canopies. Ann. Rev. Fluid
Mec. 13: 97-129.
Roberts JM, Cabral OMR, Costa JP, McWilliam A-LC Sa TDdA. 1996. An overview of the
leaf area index and physiological measurements during ABRACOS, In Amazonian
Deforestation and Climate. Gash JHC, Nobre CA, Roberts JM and Victoria RL Eds.,
Wiley, 287-306, Chichester.
Robinson SK. 1991. Coherent Motions in the Turbulent Boundary Layer. Ann. Rev. Fluid
Mec. 23: 601-639.
Sá LDA, Pachêco VB. 2006. Wind Velocity above and inside Amazonian Rain Forest in
Rondonia. Revista Brasileira de Meteorologia. 21: 50-58.
46
Sakai RK, Fitzjarrald DR, Moore KE. 2001. Importance of Low-Frequency Contributions to
Eddy Fluxes Observed over Rough Surfaces. J. Appl. Meteorol. 40: 2178-2192.
Silva Dias MAFS, Rutledge S, Kabat P, Silva Dias P, Nobre C, Fisch G, Dolman H, Zipser E,
Garstang M, Manzi A, Fuentes J, Rocha H, Marengo J, Plana-Fattori A, Sá LDA, Avalá
RCS, Andreae M, Artaxo P, Gielow R, Gatti L. 2002. Clouds and rain processes in a
biosphere atmosphere interaction context in the Amazon Region. J. Geophys. Res. 107,
8072.
Sun J, Mahrt L, Nappo C, Lenschow DH. 2015. Wind and Temperature Oscillations
Generated by Wave-Turbulence Interactions in the Stably Stratified Boundary Layer. J.
Atmos. Sci., 72: 1484-1503.
Thom AS, Stewart JB, Oliver HR, Gash JHC. 1975. Comparison of aerodynamic and energy
budget estimates of fluxes over a pine forest. Q. J. R. Meteorol. Soc. 101: 93-105.
Tóta J, Fitzjarrald DR, Silva Dias MAF. 2012. Amazon Rainforest Exchange of Carbon and
Subcanopy Air Flow: Manaus LBA Site – A Complex Terrain Condition. The Scientific
World Journal. 165067. doi:10.1100/2012/165067
Vickers D, Mahrt L. 1997. Quality Control and Flux Sampling Problems for Tower and
Aircraft Data. J. Atmos. Oceanic Technol. 14(3): 512-526.
Viswanadham Y, Molion LCB, Manzi AO, Sá, LDA, Silva Filho VP, André RGB, Nogueira
JLM, dos Santos RC. 1990. Micrometeorological Measurements in Amazon Forest
during GTE-ABLE-2A Mission. J. Geophys. Res.95:13,669-13,682.
von Randow C, Sá LDA, Gannabathula PS, Manzi AO, Arlino PR, Kruijt B. 2002. Scale
variability of atmospheric surface layer fluxes of energy and carbon over a tropical rain
forest in southwest Amazonia 1. Diurnal conditions. J. Geophys. Res: Atmospheres
(1984–2012), 107(D20): LBA-29.
Yi C. 2008. Momentum Transfer within Canopies. J. Appl. Meteorol. Climatol. 47: 262-275.
Zeri M, Sá LDA, Nobre CA. 2013. Estimating buoyancy heat flux using the surface renewal
technique over four Amazonian forest sites in Brazil. Boundary-layer meteorol. 149(2):
179-196.
Zeri M, Sa LDA. 2010. The impact of data gaps and quality control filtering on the balances
of energy and carbon for a South west Amazon forest. Agric. For. Meteorol.150: 1543–
1552.
47
Capítulo 3
__________________________________________________
Dias-Junior, C.Q. Sá, L.D.A. Marque Filho,
E.P.
Mauder,
M.
Manzi,
A.O.
2015.
Turbulence regimes in the stable boundary
layer above and within the Amazon forest.
Submetido para Boundary Layer Meteorology.
48
Turbulence regimes in the stable boundary layer above and
within the Amazon forest
Cléo Q. Dias-Junior  Leonardo D. A. Sá  Edson. P. Marques Filho  Matthias Mauder 
Antonio. O. Manzi
Abstract The structure of atmospheric turbulence is analyzed based on the existence of three
different night-time turbulent regimes observed in the Amazon forest, classified according to
criteria proposed by Sun et al. (Journal of the Atmospheric Sciences, 2012, Vol. 69, 338-351):
regime 1) weak turbulence, low wind speed; regime 2) strong turbulence, with high wind
speed, and regime 3) intermittent turbulence events. Therefore, we have investigated some of
the main statistical characteristics of turbulent regimes. In situations with strong winds and
high values of turbulent kinetic energy (4% of cases) sensible heat fluxes are about 40 times
higher than the ones under light winds and low turbulent kinetic energy values (95% of
cases). Furthermore, the inflection point height in the wind profile and shear length scale
𝐿ℎ =
𝑢ℎ
𝑑𝑢⁄
𝑑𝑧
(where 𝑢ℎ is the mean wind velocity at canopy top) increases with the regime 2,
with the occurrence of strong mixing in the atmospheric boundary layer. In addition the
coherent structure time scale in the regime 2 is greater than regime 1. It is suggested that,
when the wind is strong enough, the forest-atmosphere exchanges are strongly influenced by a
vortex whose center of symmetry is located just above the top of the forest canopy. Regime 3
is essentially nonstationary according with a criterion in the literature.
Keywords: Amazon forest
•
Coherent structures
•
Inflection-point instability
•
Nocturnal
boundary layer • Turbulent regime
1 Introduction
The characteristics of the nocturnal boundary layer (NBL) have received considerable
attention from a number of researchers, and significant scientific progress has been achieved
based on high-quality data obtained during large-scale experimental campaigns such as the
SABLES-98 (Cuxart et al. 2000), CASES-99 (Poulos et al. 2002), and LBA (Silva-Dias et al.
2002) projects, undertaken in the late 1990s. Despite several interesting investigations of
49
biosphere–atmosphere exchanges in the tropics (e.g., Shuttleworth et al. 1985, Fitzjarrald and
Moore 1990, Viswanadham et al. 1990), a number of important aspects of the turbulent
processes that occur above and within forests during the night have not been addressed, e.g.:
i) the existence of different classes and/or regimes of nocturnal turbulence, as proposed by
Van de Wiel et al. (2003), Cava et al. (2004), Sun et al. (2012) for experimental sites in the
mid-latitudes; ii) the existence of instability of the inflection point in the wind profile and
occurrence of mixed-layer similarity, and the characteristics of turbulent exchanges under
these conditions (Högström and Bergström 1996, Raupach et al. 1996, Finnigan 2000); and
iii) the importance of considering nonstationary flow as a subject of scientific interest, in
addition to the need for classifying the characteristics of flows in the atmospheric surface
layer (ASL), according to the stationarity indices discussed by Mahrt (1998, 2007), Van de
Wiel et al. (2003), Zeri et al. (2013, 2014), Cava et al. (2014), among others.
The intention of this study was to combine the three objectives listed above, i.e., to
attempt to understand how the instability of the inflection point, associated dominant
turbulent eddy (DTE) near the forest–atmosphere interface, and consequent occurrence of the
mixed-layer similarity are manifested under different turbulent regimes and different
conditions of stationarity. The method of Sun et al. (2012) was used (hereafter, SUN12) for
the detection of the distinct types of nighttime turbulence regimes. This method takes into
account the possibility of external agents such as convective clouds acting on the ASL and
disturbing its turbulent fields (Garstang et al. 1998, Garstang and Fitzjarrald 1999, Betts et al.
2002, 2009).
During turbulent events under a typical humid scenario of the tropics, particularly with
the presence of convergence zones above the regions where the turbulence is studied (with the
consequent increase in the incidence of convective clouds, storms, updrafts, and downdrafts),
the nonstationarity of turbulent fields often occurs. Such situations are important regarding
the generation of peculiar turbulence field patterns in the NBL (Mahrt 2007), and the aim of
this study was to show that one of the turbulent regimes proposed by SUN12 corresponds to
situations in which the nonstationarity indices are very high.
Robinson (1991), Raupach et al. (1996), Finnigan (2000) have discussed the
importance of the role played by the DTE in the dynamics of the transfer process at the
forest–atmosphere interface. Understanding how the dominant vortex (as named by Cava and
Katul 2008) operates at the forest–atmosphere interface, and determining its effects both on
the vertical profiles of scalar and vector quantities above and within the canopy and on the
variability of turbulent flows, are of great interest for several reasons. One reason is related to
50
better understanding of the variability of trace gas concentrations in regions surrounded by
forest (Andreae et al. 2015), including the residence time associated with the existence of
certain chemical compounds within the forest canopy (Foken at al. 2012). Furthermore, it is
interesting to expand comprehension of the biogeochemical processes that occur within forest
environments in order to provide more realistic and appropriate parametrizations for use in
ecophysiological models (Costa et al. 2010, Von Randow et al. 2013). Another reason
concerns the need to better understand the processes involving extreme climatic events in
tropical regions (Nepstad et al. 2004, Zeri et al. 2014), which would help improve public
policies aimed at mitigating the socioeconomic effects of adverse meteorological phenomena,
as well as providing grounds for financial support for the improvement of meteorological and
climate models. Finally, better understanding is required of the theoretical aspects related to
the organization of turbulence in the forest–atmosphere interface under different regimes,
such as on scales associated with the occurrence of coherent structures (CS) (Collineau and
Brunet 1993, Dias-Júnior et al. 2013), in addition to the deepening of the understanding of the
genesis of some nonlinear phenomena in the NBL, as reported by Fitzjarrald and Moore
(1990), Costa et al. (2011), among others.
2 Experimental Setup and dataset
The data were collected above the Rebio Jarú forest reserve in the south-western
Amazon (Andreae et al. 2002). Detailed descriptions of the meteorological tower
instrumentation and aspects of the regional climate may be found in Dias-Junior et al. (2013).
Briefly, the data were collected by instruments arranged on a 60-m-high
meteorological tower (Fig. 1), as part of the LBA wet season intensive campaign in the
western Amazon (Silva-Dias et al. 2002). As mentioned by von Randow et al. (2002), at the
top of the tower, a 3-D sonic anemometer was installed on a vertical beam, 67 m above the
forest floor. This instrument provided measurements of the three wind components (u, v, w)
and the sonic virtual air temperature (Tv ) at 16 Hz. In addition, vertical profiles of the wind
speed, temperature, and relative humidity were measured with a sampling rate of 0.1 Hz. The
wind speed data were measured by 10 cup anemometers (Low Power A100L2, Vector
Instruments Inc.) arranged at heights to provide information with suitably accurate resolution
for determining the inflection point height (zi ).
51
a)
b)
Fig 1 a) Photograph of the meteorological tower erected in the Rebio-Jarú forest reserve; b) schematic diagram
showing the sonic and cup anemometers arranged on the tower and their relationship to the forest canopy.
In addition, data from 11 thermometers and hygrometers (model HMP45C-L150
Väisälä), installed in aspirated weather shelters (model RM Young 43408), were available for
obtaining the vertical temperature and moisture profiles, respectively, both above and within
the canopy. The location of each instrument is shown in Table 1.
Instruments
𝑇1, 𝑞1, 𝐴1
𝑇2, 𝑞2, 𝐴2
𝑇3, 𝑞3, 𝐴3
𝑇4, 𝑞4, 𝐴4
𝑇5, 𝑞5, 𝐴5
𝑇6, 𝑞6, 𝐴6
𝑇7, 𝑞7, 𝐴7
𝑇8, 𝑞8, 𝐴8
𝑇9, 𝑞9, 𝐴9
𝑇10, 𝑞10, 𝐴10
𝑇11, 𝑞11
Height (m)
58.35, 58.45
54.90, 55.00
50.45, 50.55
47.60, 47.70
42.80, 42.90
37.65, 40.25
32.75, 37.80
30.95, 32.85
25.45, 25.65
14.30, 14.30
5.00
Table 1 Meteorological instruments location at the Rebio-Jarú reserve’s tower: thermometers (𝑇), hygrometers
(𝑞) and anemometers (𝐴). The thermometers and hygrometers are at the same heights.
52
Data obtained on 14 typical nights were analysed (Julian days 38, 40–45, and 50–56,
1999). The time series were partitioned into 5-min datasets, according to the suggestions of
Sun et al. (2002) and and Vickers et al. (2010), to improve the statistical analyses of the NBL
turbulence regimes. Thus, from the investigated 14 nights, 1490 datasets were available. To
verify the quality of the fast-response turbulent data and in order to perform subsequent
analyses, the following procedures were implemented: i) spikes within the time series were
removed according to the methodology of Vickers and Mahrt (1997); ii) the sampling rate of
the data was reduced from 16 to 1 Hz to reduce computation time (Thomas and Foken 2007);
and iii) linear trends were removed from the turbulent time series prior to performing the CSdetection procedure.
3 Methods
We used turbulent data measured at a fast-response sampling rate to calculate the
̅ = u2 + v 2 )1/2 . This methodology is similar to that used
average horizontal wind speed (U
by SUN12 to characterize nocturnal turbulent regimes above the Rebio Jarú forest reserve.
However, while that work used VTKE = √TKE as the characteristic scale of the turbulent
velocity (TKE is the turbulent kinetic energy), in this paper, the characteristic scale is defined
as the standard deviation of w (σw ). This was adopted because according to Acevedo et al.
(2009), σw is more appropriate than VTKE because it is less affected by the submeso processes
(Mahrt et al. 2008) that are very active in the Amazon (von Randow et al. 2002, Acevedo et
al. 2014). After this procedure, it is possible to classify the available datasets into three
turbulent regimes (which will be explained later).
3.1 Inflection point height in the wind profile and wind shear's length-scale (𝐿ℎ )
This section is based mainly on the work of Dias-Júnior et al. (2013), who developed
code to estimate the value of zi . Thus, a third degree polynomial function was developed for
the nine available measurements of the wind profile and a least square numerical best fit
performed. Once the best-fitting function was determined, it was possible to calculate the
zi value, based on which a length scale associated with the wind shear (Lh ) could be
calculated (Raupach et al. 1996, Sá and Pachêco 2006):
Lh =
̅̅̅̅
uh
̅̅̅̅
du
⁄
(
dz)|h
,
(1)
53
̅̅̅̅
where uh is wind speed at the canopy-height (h), and (du⁄dz)| is the vertical gradient of the
h
mean wind speed over h.
It is noteworthy that both Raupach et al. (1996) and Brunet and Irvine (2000) had
relative success using the shear length scale to express some universal characteristics of the
atmospheric flow over various types of vegetation canopy.
3.2 Turbulent kinetic energy dissipation
The TKE dissipation rate per unit mass (𝜀) expresses quantitatively the conversion of
turbulent mechanical energy into heat when the near-surface atmospheric flow acts against
viscous shear forces (Kaimal and Finnigan 1994, pp 26-27). A process widely used to
estimate the value of 𝜀 is based on the validity of Taylor’s hypothesis (Stull 1988, pp 5-6) and
on the relationship established by Kolmogorov (Stull 1988, pp.390) for the inertial subrange
part of the turbulence spectrum regarding the 𝑥-component of the wind (Stull 1988, 390 pp):
𝑆𝑥 (𝑘) = 𝛼𝑥 𝜀 2/3 𝑘 −5/3
(2)
where 𝑆𝑥 (𝑘) is the power spectral density corresponding to the wave number 𝑘 and 𝛼𝑥 is
Kolmogorov’s constant, the value of which depends on the wind speed component studied.
Here, the longitudinal component of the wind speed 𝑢 was used, which yielded 𝑆𝑢
values from an inertial subrange with edges between 1.0 and 2.5 Hz. This is entirely within
the range of occurrence of the inertial subrange according to Bolzan and Vieira (2006), whose
obtained results based on the same experimental data used here. We adopted a value of 𝛼𝑢 =
12.52 (Kaimal and Finnigan 1994, pp 64).
3.3 Time Scale of Coherent Structures (CS)
According to Gao and Li (1993), the scale of occurrence of CS in a time series may be
determined using the scale variance of the wavelet coefficients of the available data. The
description of the wavelet methodology applied here can be found in Thomas and Foken
(2005).
After preparation of the 5-min files, a continuous 1-D wavelet transform was used,
which is defined when applied to a given signal 𝑓(𝑡) as:
𝑊𝜓 𝑓(𝑎, 𝑏) =
where 𝑎 ∈ ℛ + and 𝑏 ∈ ℛ.
1 +∞
𝑡−𝑏
∫ 𝑓(𝑡)𝜓 ( 𝑎 ) 𝑑𝑡
√𝑎 −∞
(3)
54
The scale decomposition was performed by translation and dilatation of only one
“mother wavelet”, which was stretched or compressed and displaced along the time line to
generate a family of “daughter wavelets”. These can be expressed as the function of two
parameters: one for their scale (𝑎) and other for their time position (𝑏).
The Morlet complex function (Eq. 4) was used because it is more suitable for the time
scale analysis of CS, as discussed in depth by Thomas and Foken (2005):
𝜓 (𝜂) = 𝜋
1⁄
4
𝑒 𝑖𝜔0 𝜂 𝑒 −𝜂
2 ⁄2
(4)
where 𝜂 is the dimensionless time parameter and 𝜔0 is the dimensionless frequency.
The CS time scale corresponds to the one for which the wavelet coefficient variance
𝜎 (𝑎, 𝑏) reaches its maximum value:
2
𝜎(𝑎, 𝑏) = ∫|𝑇𝜓 𝑓(𝑎, 𝑏)| 𝑑𝑏
(5)
where T f (a, b) is the Morlet wavelet transform.
Thus, if atmospheric transport is dominated by coherent eddies of a certain scale, as
appears to be the case concerning the atmospheric flow above the Amazonian forest (Zeri et
al. 2013, 2014), the corresponding power spectrum should exhibit a distinct peak at that scale.
Accordingly, the event duration of CS (𝐷𝑒 ) was inferred from the scale 𝑎𝑒 of the clearly
expressed maximum in the wavelet spectrum, the peak frequency of the mother wavelet
ω0ψp,1,0 , and the time resolution of the time series (Thomas and Foken 2005),
𝐷𝑒 =
𝑎𝑒 ∆𝑡𝜋
ω 0ψ
(6)
p,1,0
3.4 Stationary conditions
Time series are considered stationary when the associated statistical moments (e.g.,
mean, variance, skewness, and curtosis) do not depend on the initial time of the analysed
series (Panofsky and Dutton 1984, pp 39). These tests were undertaken because it is known
that in the NBL, many phenomena such as gravity waves, density currents, low-level jets,
cloud passage, and katabatic winds occur (Mahrt 1998, Poulos et al. 2002, Sun et al. 2002,
2004, Mahrt 2007, Zeri and Sá 2011). These commonly alter the mean flow and can cause it
to become nonstationary, which can hinder robust estimation of the statistical moments under
such conditions (Mahrt 2007, Zeri et al. 2014).
55
In this work, the methodology proposed by Mahrt (1998) was used to classify the time
series according to its stationary or nonstationary characteristics. The process undertaken was
as follows:
i) The 5-min time series were divided into five 1-min intervals (𝐼 records);
ii) Each 1-min interval was divided into five 12-s subintervals (𝐽 subrecords);
iii) Turbulent fluxes were calculated for all 𝐼 and 𝐽 intervals. Here, the sensible heat flux
(𝐻) was calculated because the analysis of the buoyancy effect was of considerable interest in
this study; and
iv) Finally, the standard deviation corresponding to the heat fluxes associated with
segments 𝐽 (𝜎𝑤𝑖 ) and 𝐼 (𝜎𝑤𝑡𝑏 ) were calculated.
The nonstationarity (𝑁𝑅) for each 5-min time series was defined by the index (Mahrt
1998):
𝑁𝑅 =
𝜎𝑏𝑡𝑤
𝜎𝑤𝑖
(7)
For stationary conditions, 𝑁𝑅 approaches unity. In this work, for classification
purposes, time series for which 0.5 < 𝑁𝑅 < 2.0 were considered stationary. It should be
remembered that although 𝑁𝑅 does not result from a statistically exact estimation, it is very
useful for separating time series according to their characteristics toward stationarity.
4 Results
4.1 Turbulent Regimes
̅ for the fast-response data measured
Figure 2 shows the relationship between 𝜎𝑤 and 𝑈
at a height of 67 m above the forest floor of the Rebio Jarú reserve. Each point shown in Fig.
2 corresponds to the calculations using perturbations from the 5-min means (Sun et al. 2004).
A clear distinction between the point-clusters corresponding to turbulent regimes 1 and 2 can
be seen with regard to their respective fitted straight lines. The slope of the straight line
corresponding to regime 1 (𝛼𝐼 ), is clearly less than that corresponding to regime 2 (𝛼𝐼𝐼 ). It is
̅ values of
also noticeable that the point cluster corresponding to regime 3, for the same 𝑈
regime 1, show higher 𝜎𝑤 values than regime 1.
The value of the threshold wind speed (𝑉𝐿 ) that separates the regions in which regimes
1 and 2 are dominant was estimated visually. Regime 1, represented by the black circles,
̅ to reach 𝑉𝐿 (≈3.0 m s−1). In regime 2,
presents weak 𝜎𝑤 values, which increase slightly with 𝑈
56
̅ starting from 𝑉𝐿 . For
represented by the blue circles, values of 𝜎𝑤 increase quickly with 𝑈
improved visualization of the data clusters of the turbulent regimes, least squares best fits
were applied to obtain the straight lines corresponding to the data under regimes 1 and 2.
Fig 2 Standard deviation of the vertical velocity (𝜎𝑤 ), a characteristic turbulent velocity scale as a function of the
wind speed measured at 67 m height, corresponding at 14 nights. Black, blue and red circles correspond
respectively to regime 1 (low wind and weak turbulence), regime 2 (high wind and strong turbulence) and
regime 3 (intermittent turbulence events).
According to SUN12, turbulent regime 3 (red circles) could be associated with
turbulent events generated by intermittent top-down movements, characterized by strong
downward movements of air. This objective of this work was to contribute to the physical
interpretation of SUN12’s turbulent regimes above tropical forests, including regime 3 with
its nonstationary characteristics.
To determine the value of 𝑉𝐿 , estimations of 𝜎𝑤 were plotted against 𝑈 for each
interval of 0.5 m s−1 over the entire available dataset. It was observed that in the region of 𝑉𝐿
̅. All situations
= 3.0 m s−1, an abrupt change in the variation of 𝜎𝑤 occurred with respect to 𝑈
in which the wind speed was above the threshold of 3.0 ms−1 were associated with turbulent
regime 2.
To separate the data belonging to regime 3 from those belonging to regime 1, the
̅ = 0 to 𝑈
̅ = 𝑉𝐿 . Based on
standard deviation of 𝜎𝑤 was determined for various intervals from 𝑈
these calculations, all data for which 𝜎𝑤 > 4.5 were defined as belonging to regime 3, i.e., the
remaining data were considered as belonging to turbulent regime 1.
After identifying the nighttime turbulent regimes from the 1490 analysed time series,
95.1% of them were associated with regime 1, 3.4% with regime 2, and only 1.5% with
57
regime 3 (Table 2). Therefore, it is clear that the NBL of the Amazon is largely characterized
by a regime of light winds and low TKE, although the total contributions to the global 𝐻 from
regime 2 exceed those provided by regime 1, as is shown later in this paper.
Number of
events
̅ (m s-1)
𝑼
𝝈𝒘 (m s-1)
Regime 1
Regime 2
Regime 3
1417
51
22
1.39
0.10
4.53
0.50
1.10
0.31
Table 2 Some characteristics of the nocturnal turbulent regimes above the Rebio-Jarú reserve.
Stationarity tests were performed for the available time series datasets. Figure 3 shows
those situations where the time series were classified according to the 𝑁𝑅 index (represented
by green dots). It can be seen that the degree of 𝑁𝑅 of regime 3 is considerably larger than
regimes 1 and 2.
As can be seen in Fig. 3, the data of regime 3 are associated with time series that do
not satisfy the stationarity condition well. These data also deviate from the data clusters
related to regimes 1 and 2. This appears associated with the physical conditions in which the
predominate interaction of the atmospheric flow with the underlying vegetation cover, is in
the presence of strong vertical wind shear induced by surface roughness associated with the
presence of the forest canopy. However, in situations associated with regime 3, factors
unrelated to local forest–atmosphere interaction processes seem to play a dominant role.
Fig 3 Similar to Fig 2. Black circles and green dots correspond, respectively to stationary 5min periods and nonstationary 5min period.
The next section shows that the turbulent fluxes of scalars are considerably higher
during regime 2 compared with those observed during regime 1.
58
4.2 Sensible Heat Flux
Data from a typical evening during the 1999 rainy season (Julian days 45/46) were
used to investigate the differences between 𝐻 during the occurrence of regimes 1 and 2. Thus,
132 time series of 5-min datasets were available, but only 106 time series met the stationarity
criteria and were used in the following analyses.
That night, there was a total 𝐻 of approximately −2.35 × 105 J m−2, integrated
throughout the entire nighttime period. Regime 1 persisted for 81% of the reporting period
and accounted for 28% of 𝐻 (Table 3). Conversely, regime 2 persisted for 19% of the studied
period and accounted for 72% of the total 𝐻.
Turbulent regimes
Regime 1
Regime 2
Full 𝑯 (J m-2)
– 0.65 × 105
– 1.7 × 105
Average 𝑯 (W m-2)
– 1.82
– 43.62
Table 3 Full 𝐻 integrated throughout the entire night-time period and average values of 𝐻 for both regime 1 and
regime 2.
The number of occurrences of regime 1 is far greater than the instances of regime 2.
However, when regime 2 does occur, it contributes more significantly to 𝐻 in comparison
with regime 1. This will become clearer in Sect. 4.5, where a case study of regime 2 revealed
that the forest canopy is heated and has a considerable fall in its relative humidity over a
period of about 20 min.
It should be noted that Fitzjarrald and Moore (1990) used data from the Ducke reserve,
located in the central Amazon, to characterize the forest–atmosphere nocturnal sensible heat
exchanges. They found that in conditions of relatively strong winds, 𝐻 was >10 times its
average value throughout the analysed period. They also found that the situations of strong
wind and considerable 𝐻 were intermittent, occurring for only 3% of the entire period
analysed. However, they did not conduct their analysis based on different turbulent regimes,
which is why they could not specify the conditions under which the phenomenon of the
considerable increase in 𝐻 occurred.
According to Raupach et al. (1996) the DTE would present a centre of symmetry at the
inflection point location. Therefore, a variation in the value of 𝑧𝑖 should have important
dynamical consequences at the forest–atmosphere interface, where eddies centred at the
inflection point could possibly penetrate into the canopy, which might result in a buildup in
the values of 𝐻 in the region of occurrence of the DTE.
59
4.3 Inflection Point Height, Wind Shear, and Dissipation Length Scale
Several researchers have shown that the atmospheric turbulent flow above high
vegetation is dominated by strong vertical wind shear, which is generated mainly at the
forest–atmosphere interface (Paw U et al. 1992, Raupach et al. 1996, Brunet and Irvine 2000,
Finnigan 2000, Thomas and Foken 2007). It exhibits high efficiency in the absorption of the
horizontal momentum of the flow, which results in the generation of an inflection point in the
wind profile (Raupach et al. 1996, Brunet and Irvine 2000, Sá and Pachêco 2006, Thomas and
Foken 2007, Dias-Junior et al. 2013). The depth of the wind shear layer might be associated
with length scale 𝐿ℎ (Dupont and Brunet 2009).
This absorption of momentum by the canopy occurs because of the impact of the flow
against the vegetation structure, which generates turbulent wakes behind the bluff bodies and
dissipates TKE by converting it into heat. Therefore, it is interesting to obtain the rate at
which TKE is lost by calculating the TKE dissipation rate (𝜀). Therefore, the value of 𝜀 was
estimated above the treetops (67 m), because fast-response turbulent data were available at
this level from the sonic anemometer. However, as discussed above, it was not possible to
estimate the value of 𝜀 in the region closest to the forest–atmosphere interface, where it would
be expected that the action of the DTE would be most intense. Nevertheless, the variation of 𝜀
associated with the change of turbulent regime should provide interesting insights regarding
the characteristics of each regime.
Figures 4a–c show the probability density functions for the values of the parameters
𝑧𝑖 , 𝐿ℎ , and 𝜀 respectively, under turbulent regimes 1 (dashed line) and 2 (solid line). It can be
seen from Fig. 4a that values of 𝑧𝑖 are clustered approximately around 37 and 39.5 m for
regimes 1 and 2, respectively. Figure 4b shows that the mean values of 𝐿ℎ are 7.5 and 14 m
for regimes 1 and 2, respectively. Figure 4c shows that there is a clear difference between the
𝜀 values found for regimes 1 and 2. Thus, it may be concluded that for regime 2, the 𝜀 values
are at least one order of magnitude greater than for regime 1.
It should be noted that the 𝑧𝑖 values under regimes 1 and 2 appear to present a distinct but
relatively small difference. This difference might result in a considerable increase in the radius of
the DTE for regime 2 in comparison with regime 1 (the centre of the DTE should be in 𝑧𝑖 ). Thus,
such a difference has important implications regarding both the capability of the DTE to
penetrate downwards (regime 2) or not (regime 1) deep into the canopy and the associated
forest–atmosphere exchange processes.
60
a)
b)
c)
Fig 4 Probability Density Functions (PDFs) for: a) Inflection point height, 𝑧𝑖 , (m); b) Wind shear length-scale,
𝐿ℎ , (m); c) logarithm of the viscous dissipation, 𝜀, (m2 s-3). Dashed lines correspond to regime 1’s occurrences
and full lines correspond to regime’s 2 ones.
When interpreting the above findings, it is important to consider the results of other
researchers who also found variations in the height of the inflection point (𝑧𝑖 ), above tall
vegetation. For example, Thomas and Foken (2007), using data from a boreal forest in
Germany, found that the 𝑧𝑖 value varies as the direction of the average wind changes.
However, Dupont and Patton (2012), using data obtained from a deciduous forest in
California, found that the 𝑧𝑖 value changes depending on whether the trees are in leaf.
Other results that deserve attention are those of Poggi et al. (2004). They used flow
simulations in a wind tunnel to study the turbulent flow over canopies with different degrees
of roughness. They noted clear inflection points in the vertical wind profiles of simulations of
dense canopies; however, for sparse canopies, they were unable to observe such inflection
points clearly. Nevertheless, according to Poggi et al. (2004), the intensity of the inflection in
the wind profile influences the organization of turbulence above forest canopies. Moreover,
the existence of strong vertical wind shear at the forest–atmosphere interface (and the
consequent existence of 𝑧𝑖 ) is also a necessary condition for the emergence of Kelvin–
Helmholtz instabilities, as discussed by Cheng et al. (2005) in their study regarding the
performance of the Monin–Obukhov Similarity Theory in each of the four types of physical
transient phenomena during the nights of the CASES-99 experiment. In addition, Finnigan
(2000) states that inflection points in the vertical wind profile are typical characteristics of an
atmospheric flow above tall vegetation and that their presence suggests the validity of the
mixing-layer analogy, with flow layers that have different average speeds above and below 𝑧𝑖 ;
thus, reinforcing the findings presented by Raupach et al. (1996).
61
4.4 Time Scale of Coherent Structures (CS)
CS are critical in the transfer of momentum and scalars at the forest–atmosphere interface
(Thomas and Foken 2007, Steiner et al. 2011). Next to the treetops, such structures appear
associated with an intense wind shear that is generated by the impact of the atmospheric flow
on the canopy (Finnigan 2000, Dias-Júnior et al. 2013).
In this study, the time scales (𝐷𝑒 ) of CS of 𝑢, 𝑤, and 𝑇 were identified as shown in
Figs. 5a–c, respectively. The dashed and continuous lines in Figs. 5a–c correspond to events
in regimes 1 and 2, respectively. It can be seen that the values of 𝐷𝑒 are significantly higher
for regime 2 in comparison with regime 1, particularly for variables 𝑢 and 𝑇. It is clear that
the values of 𝐷𝑒 in regime 1 for 𝑢, 𝑤, and 𝑇 are about 68, 47, and 64 s, respectively, whereas
they are about 87, 54, and 76 s, respectively, for regime 2.
According to Thomas and Foken (2005), the spectra of scalars are closer to the spectra
of the horizontal velocity in the low-frequency region, in comparison to the vertical velocity.
This leads to the conclusion that transport through low-frequency processes, such as the CS, is
generally related more to horizontal transport. This behaviour could explain the similarities
between the 𝐷𝑒 values of 𝑢 and 𝑇. Gao and Li (1993) offered another interesting explanation
that used the time series of 𝑇 and 𝑤 to compare the time scales of the CS for different levels
above and within a deciduous forest at Camp Borde, Canada. They observed that 𝑤-structures
were shorter-lived than those of 𝑇. They explained such a result as a consequence of
temperature changes caused primarily by nonlocal transport associated with movements
induced by updrafts and downdrafts. However, changes in 𝑤 can result both from organized
movements and from atmospheric flow disturbances linked to turbulence generated by local
interactions.
62
a)
b)
c)
Fig 5 The same of the Fig. 4 but for the coherent strucuture time scale correspond to: a) horizontal wind velocity
streamwise componente, 𝑢; b) vertical wind velocity component, 𝑤; c) temperature, 𝑇. Dashed lines correspond
to regime 1’s occurrences and full lines correspond to regime’s 2 ones.
4.5. Case Study
In this section, special attention is given to an example of turbulent regime 2 (Julian
day 45, from 2130 to 2150 local time) in which the vertical profiles of 𝑈 (wind speed), 𝑇
(temperature), and 𝑞 (humidity) are shown for a long-lasting event (20 min) of turbulentregime 2. This is based on data obtained at 10-s intervals, from above and within the forest
canopy, using the meteorological tower in the Rebio Jarú forest reserve (see Table 1). It
should be noted that less attention is given to the occurrence of regime 1 because it is the
dominant state of the Amazonian nighttime period, and thus it has already been studied often
(Fitzjarrald and Moore 1990, Kruijt et al. 2000).
4.5.1. Continuous Profiles of Temperature, Relative Humidity, and Wind Speed
Figures 6a–c show the continuous vertical profiles of temperature, relative humidity,
and wind speed, respectively. A number of features can be observed during the occurrence of
a regime-2 event: i) heating of the air within the canopy (Fig. 6a); ii) a decrease of relative
humidity within the canopy (Fig. 6b); and iii) an increase in wind speed both above and
within the forest canopy (Fig. 6c).
63
a)
Temperature (oC)
b)
Relative humidity (%)
64
c)
Wind speed (m/s)
Fig 6 Contour plots regarding the evolution of: a) Temperature; b) relative humidity and c) wind speed for a case
study concerning the turbulent regime 2 (Julian day 45 from 21:30 to 21:50 local time).
There are a number of noteworthy results discernible in Figs. 6a and b. For example,
the height of approximately 32 m denotes the clear separation between the processes above
and below the forest canopy. This level probably corresponds to what was called the
“thermodynamic height” of the forest (ℎ𝑡 ) by Cava and Katul (2008). Figure 6a shows a clear
decrease and Fig. 6b shows a gradual increase in the thicknesses of the “blue bands”,
indicating temperatures between 24.0 and 24.4 °C and relative humidity values between 92%
and 93.5%, respectively. Within the forest canopy, there is a tendency for this environment in
warm and dry at all the observed levels. In Fig. 6b, in addition to the blue band at ℎ𝑡 , there is
also another distinct line at the height of approximately 47 m. The blue band at approximately
32-m height is linked to the average height of the forest canopy and its interface with the
atmosphere.
It is easy to understand why the minimum value of the vertical temperature profile is
found at the canopy top, i.e., it is a consequence of the negative local radiation balance.
Clearly, there is a net loss of energy in the treetop region through radiative processes, in
which the upward longwave radiation component is not completely offset by the downward
longwave component. Molion (1987), in his analysis of the diurnal variability of the energy
65
budget over the Amazon rainforest in the Ducke reserve (central Amazon), has shown that the
deficit in the energy balance due to longwave radiation is of the order of 40 W m−2 at virtually
all times of a typical day.
It should be noted that Shuttleworth et al. (1985) were among the first to analyse the
evolution of temperature profiles above and within the Amazon rainforest. For this, they used
data from a 45-m-high tower installed in the Ducke reserve in the central Amazon. According
to them, in the absence of convective storms and episodes of rain, i.e., under dry conditions,
the profiles of temperature, humidity, and moisture deficit have similar behaviours in two
layers that are commonly decoupled during the night: “in the lower 2/3 of the canopy is
partially decoupled from that at higher levels”. This decoupling between the two layers is
associated with a decrease in turbulent activity above the canopy, such that the radiative
processes in the near-surface lower layer, among the internal layers of the vegetation, are
responsible for the equilibrium of the heat balance. This would be the prevailing situation for
those periods during which turbulent regime 1 is dominant. However, in turbulent regimes 2
and 3, such a situation does not hold. In regime 2, the strong winds and action of the DTEs
penetrate into the canopy and disturb the thermal equilibrium, whereas in regime 3, top-down
air movements, which could be associated with convective clouds and downdraughts,
similarly disturb the thermal equilibrium.
The above analysis of Shuttleworth et al. (1985) regarding the nighttime period was
focused mainly on hourly averages and there has been no attempt to separate them according
to the characteristics of the turbulent regime. However, Fitzjarrald and Moore (1990) have
studied nocturnal data obtained from the same location of the Ducke reserve and observed an
alternation between periods of intense turbulent exchanges and weak turbulent transfers, but
they did not expand their study into a quantitative analysis concerning the differences between
these two processes. Mafra (2014) used data from an 80-m-high tower erected in the Uatumã
reserve in the central Amazon (ATTO Project) and applied the SUN12 methodology to study
the seasonal variability of CO2 fluxes in each of the three turbulent regimes; substantial
differences were found between the turbulent fluxes in regimes 1 and 2.
4.5.2. Temperature, Relative Humidity, and Wind Speed Profiles
For better visualization of the vertical profiles discussed above and their variations over a
period of about 20 min (related to the studied case concerning the occurrence of turbulent
regime 2), Figs. 7a and b present the average temperature profiles for the first 5 min (𝑇1 ) and
last 5 min (𝑇2 ), respectively (shown in Fig. 6a, too); Fig. 7c shows their difference (𝑇2 − 𝑇1 ).
66
Figures 7d and e are similar to Figs. 7a and b, but for profiles of relative humidity, providing
(𝑞1 ) and (𝑞2 ) values, respectively, instead of (𝑇1 ) and (𝑇1 ); Fig. 7f shows their difference
(𝑞2 − 𝑞1).
It can be seen from Figs. 6a and 7a–c that at the origin of the time series (where the
regime-2 episode starts), there is a greater 𝑇-gradient between the regions located above and
below the forest canopy (Fig. 7a). However, it decreases considerably along the time line
during the occurrence of regime 2, which is particularly true for the vertical 𝑇-gradient just
above the forest canopy. Furthermore, during this episode, the vertical 𝑇-gradient within the
canopy (between 15 and 25 m) appears to increase, and the vertical 𝑇-profile, observed
between the heights of 𝑍2 = 47.5 m and 𝑍1 = 14.5 m (𝑇2 − 𝑇1 ), is approximately linear
between 15 and 50 m; this difference increases downwards until the 15-m level.
The vertical profile of relative humidity between the heights of 𝑍1 and 𝑍2 , (𝑞2 − 𝑞1 )
(Fig. 7e) also shows an approximately linear function between the heights of 15 and 50 m.
However, unlike the temperature, it can be seen that relative humidity decreases (above and
within the canopy) to the extent that the regime-2 episode evolves. Based on these
considerations, it is possible to suggest that the DTEs are capable of bringing warmer and
drier air from above into the region within the vegetation canopy.
Figures 7c and f show the positions of points 𝑃1 ≈ 14.5 m, 𝑃𝐶 ≈ 31 m, and 𝑃2 ≈ 47.5
m. It is assumed that these points correspond to the inferior edge of the DTE, forest–
atmosphere interface, and upper edge of the DTE, respectively. In the edge regions of the
DTE, greater local shear would be expected, the existence of which would be reflected in the
variables measured there. This assumption is based on the conspicuous discontinuity observed
in the 𝑇-profile (exactly at points 𝑃1, 𝑃𝐶, and 𝑃2), but less evident in the 𝑞-profiles at the
same points (𝑃1, 𝑃𝐶, and 𝑃2). Cava and Katul (2008) have shown the existence of shortcircuiting spectral effects on the atmospheric flow at the forest–atmosphere interface. Our
assumption is that a similar effect should exist in the edge regions of the DTE.
67
a)
d)
b)
e)
c)
f)
Fig 7 5 min-vertical profiles of a) mean temperature (𝑇1 ) for the earliest 5 min of the regime 2’s event; b) the
same but the latest 5 min mean temperature (𝑇2 ) of the same event. 𝑇2 – 𝑇1 values; d, e and f) the same for the a,
b and c graphics, but for the relative humidity.
5 Discussion
Little attention has been given to the existence of an inflection point in a wind profile
near vegetated surfaces. Consequently, a comprehensive theory that incorporates the
68
differences among the distinct nighttime turbulent regimes, and the physical consequences of
their existence in the surface–atmosphere exchange processes, particularly above and within
tall vegetation, is lacking. Robinson (1991) and Raupach et al. (1996) are among those
authors who have associated the existence of the inflection point to a particular instability,
which generates less-dissipative CS. Furthermore, according to Robinson (1991), there are
different types of CS: some with an axis of symmetry arranged longitudinally along the
atmospheric flow (more dissipative structures) and others with an axis of symmetry disposed
transversely to the direction of dominant atmospheric flow, which are organized like rolls
(less dissipative). It is possible that the latter are associated with the occurrence of instability,
such as that of the inflection point, or even with the presence of Kelvin–Helmholtz instability
(Starkenburg et al. 2013), possibly representing the turbulent conditions found in regime 2.
Furthermore, it has been observed that the different nocturnal turbulent regimes
presented here are related to distinct conditions of the location of 𝑧𝑖 . Based on Figs. 5–7, it is
possible to suggest that one of the differences between turbulent regimes 1 and 2 is that the
atmospheric flow associated with regime 2 presents greater inertia against surface drag forces,
in such way that the value of 𝑧𝑖 is higher, i.e., in regime 2, the upper part of the flow below 𝑧𝑖
is shifted up (see observation Stull 1988, pp 534-535, regarding the formation of small
nocturnal jets above sloping terrain). Thus, we suggest the following interpretation regarding
regime 2: the locations of the DTEs are linked to the location of 𝑧𝑖 , i.e., their structures
present the centre of symmetry at the 𝑧𝑖 level, as suggested by both Robinson (1991) and
Raupach et al. (1996).
The existence of 𝑧𝑖 determines specific features of the wind shear stress at level ℎ
(Raupach et al. 1996, Sá and Pachêco 2006, Dias-Júnior et al. 2013). This tension could be
expressed by the 𝐿ℎ length scale (length associated with the depth of penetration of the flow
into the canopy), which is closely linked with the mechanical action of the present DTE near
the top of the forest’s canopy. Thus, it is to be expected that in regime 2, the value of 𝐿ℎ ,
which is associated with a greater capability of penetration of a flow into the canopy, is higher
when compared with conditions in which there is a smaller value of 𝐿ℎ (i.e., turbulent regime
1).
Moreover, it is observed that the temperature, relative humidity, and wind speed
profiles (Figs. 6 and 7) corroborate the physical information contained in the values of 𝑧𝑖 and
𝐿ℎ , and in accordance with this, the greater speed of the atmospheric flow in regime 2 might
penetrate more deeply inside the canopy (greater 𝐿ℎ ), with a downward transfer of warmer
and drier air into the forest canopy during nighttime periods.
69
6 Conclusions
This study used data obtained from instruments on a 67-m-high tower, erected as part
of the LBA project, in Rondônia in the west of the Brazilian Amazon. The arrangement of
instruments on the tower favours research into the variability of the inflection point height in
wind profiles. The possibility of estimating the inflection point height (𝑧𝑖 ) facilitated an
investigation into the effects of the existence of DTEs immediately above the forest canopy.
Under certain circumstances, these DTEs play an active role in forest–atmosphere exchanges.
The results obtained from the analysed situations confirm the validity of the so-called
“mixing-layer analogy”. A fundamental result is the existence of nocturnal turbulent regimes
with different characteristics (action of the DTE, TKE dissipation rate, wind shear scale 𝐿ℎ ,
among others), which influence the height of 𝑧𝑖 . The variations of these characteristics from
one regime to another were investigated, and it was established that low wind regimes occur
throughout much of the night, whereas regimes with high wind and/or situations of marked
nonstationarity seldom occur and only for short periods. However, these are periods during
which turbulent fluxes show values that are approximately one order of magnitude larger than
during the regime of weak winds. Finally, it was observed that regime 3 was predominantly
nonstationary, probably because of phenomena that originate far from the surface, such as
convective clouds.
Acknowledgements This work is part of the Large-scale Biosphere-Atmosphere Experiment in Amazonia
(LBA), and was supported by the Fundação de Amparo a Pesquisa do Estado de São-Paulo (FAPESP)/process
1997/9926-9. We would like to thank the Instituto Nacional de Colonização e Reforma Agrária (INCRA) and the
Instituto Brasileiro do Meio Ambiente (IBAMA). Cléo Dias-Junior would like to acknowledge the support from
IMK-IFU, Karlsruhe Institute of Technology (Garmisch-Partenkirchen, Germany) and is grateful to the
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for his PhD’s grant and to the
Brazilian Government’s Program “Ciência sem Fronteiras” grant (process 99999.002233/2014-02). Leonardo Sá
and Edson Marques Filho are grateful to Conselho Nacional de Desenvolvimento Científico e Tecnológico
(CNPq) for their research grants, (respectively, processes 303.728/2010-8 and 308597/2012-5).
References
Acevedo OC, Costa FD, Oliveira PE, Puhales FS, Degrazia GA, Roberti DR (2014) The
Influence of Submeso Processes on Stable Boundary Layer Similarity Relationships. J
Atmos Sci 71:207-225
70
Acevedo OC, Moraes OLL, Degrazia GA, Fitzjarrald DR, Manzi AO, Campos JG (2009) Is
friction velocity the most appropriate scale for correcting nocturnal carbon dioxide
fluxes? Agric For Meteorol 149:1-10
Andreae MO, Acevedo OC, Araùjo A, Artaxo P, Barbosa CGG, Barbosa HMJ, Brito J,
Carbone S, Chi1 X, Cintra BBL, da Silva NF, Dias NL, Dias-Júnior CQ, Ditas F, Ditz
R, Godoi AFL, Godoi RHM, Heimann M, Hoffmann T, Kesselmeier J, Könemann1 T,
Krüger ML, Lavric JV, Manzi AO, Moran-Zuloaga D, Nölscher AC, Santos Nogueira
D, Piedade MTF, Pöhlker C, Pösch U, Rizzo LV, Ro CU, Ruckteschler N, Sá LDA, Sá
MDO, Sales CB, Santos RMND, Saturno1 J, Schöngart J, Sörgel M, de Souza CM, de
Souza RAF, Su H, Targhetta N, Tóta J, Trebs I, Trumbore S, van Eijck A, Walter D,
Wang Z, Weber B, Williams J, Winderlich J, Wittmann F, Wolff1 S, Yáñez-Serrano
AM (2015) The Amazon Tall Tower Observatory (ATTO) in the remote Amazon
Basin: overview of first results from ecosystem ecology, meteorology, trace gas, and
aerosol measurements. Atmos Chem Phys Discuss 15:11599-11726
Andreae MO, Artaxo P, Brandão C, Carswell FE, Ciccioli P, Costa AL, Culf AD, Esteves JL,
Gash JHC, Grace J, Kabat P, Lelieveld J, Malhi Y, Manzi AO, Meixner FX, Nobre AD,
Nobre C, Ruivo MLP, Silva-Dias MA, Stefani P, Valentini R, von Jouanne J, Waterloo
MJ (2002) Biogeochemical cycling of carbon, water, energy, trace gases, and aerosols
in Amazonia: The LBA-EUSTACH experiments. J Geophys Res 107:D20 8066
Betts AK, Fisch G, von Randow C, Silva Dias MAF, Cohen JCP, da Silva R, Fitzjarrald DR
(2009) The Amazonian boundary layer and mesoscale circulations. In: Keller M et al.
Amazonia and Global Change, Geophysical Monograph Series. Washington, D. C, pp
163-181
Betts AK, Fuentes JD, Garstang M, Ball JH (2002) Surface diurnal cycle and Boundary Layer
structure over Rondonia during the rainy season. J Geophys Res D: Atmos, 107:LBA 32
Bolzan MJA, Vieira PC (2006) Wavelet Analysis of the Wind Velocity and Temperature
Variability in the Amazon Forest. Braz J Phys 36:1217-1222
Brunet Y, Irvine MR (2000) The Control of Coherent Eddies in Vegetation Canopies:
Streamwise Structure Spacing, Canopy Shear Scale and Atmospheric Stability.
Boundary-Layer Meteorol 94:139-163
Cava D, Donateo A, Contini D (2014) Combined stationary index for the estimation of
turbulent fluxes of scalars and particles in the atmospheric surface layer. Agric For
Meteorol 194:88-103
71
Cava D, Giostra U, Siqueira M, Katul G (2004) Organised Motion and Radiative Properties in
the Nocturnal Canopy Sublayer above an Even-aged Pine Forest. Boundary-Layer
Meteorol 112:129-157
Cava D, Katul GG (2008) Spectral Short-circuiting and Wake Production within the Canopy
Trunc Space of an Alpine Hardwood Forest. Boundary-Layer Meteorol 126:415-431
Cheng Y, Parlange MB, Brutsaert W (2005) Pathology of Monin-Obukhov similarity in the
stable boundary layer. J Geophys Res 110: 1-10
Collineau S, Brunet Y (1993) Detection of Turbulent Coherent Motions in a Forest Canopy.
Part II: Time-scales and Conditional Averages. Boundary-Layer Meteorol 66:49-73
Costa FD, Acevedo OC, Mombach JCM Degrazia GA (2011) A Simplified Model for
Intermittent Turbulence in the Nocturnal Boundary Layer. J Atmos Sci 68:1714-1729
Costa MH, Biajoli MC, Sanches L, Malhado ACM, Hutyra LR, Rocha HR, Aguiar RG
Araújo AC (2010) Atmospheric versus vegetation controls of Amazonian tropical rain
forest evapotranspiration: Are the wet and seasonally dry rain forests any different? J
Geophys Res Biogeosci 115(G4)
Cuxart J, Yagüe C, Morales G, Terradellas E, Orbe J, Calvo J, Fernández A, Soler MR,
Infante C, Buenestado P, Espinalt A, Joergensen HE, Rees JM, Vilà J, Redondo JM,
Cantalapiedra IR, Conangla L (2000) Stable Atmospheric Boundary-Layer Experiment
in Spain (SABLES 98): A Report. Boundary Layer Meteorol 96, 3: 337-370
Dias Júnior CQ, Sá LDA, Pachêco VB, de Souza CM (2013) Coherent structures detected in
the unstable atmospheric surface layer above the Amazon forest. J Wind Eng Ind
Aerodyn 115: 1-8
Dupont S, Brunet Y (2009) Coherent structures in canopy edge flow: a large-eddy simulation
study. J Fluid Mech 630:93-128
Dupont S, Patton EG (2012) Influence of stability and seasonal canopy changes on
micrometeorology within and above an orchard canopy: The CHATS experiment. Agric
For Meteorol 157:11-29
Finnigan JJ (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32:519-571
Fitzjarrald DR, Moore KE (1990) Mechanisms of Nocturnal Exchange between the Rain
Forest and the Atmosphere. J Geophys Res D: Atmos 95: 16839-16850
Foken T, Meixner FX, Falge E, Zetzsch C, Serafimovich A, Bargsten A, Behrendt T,
Biermann T, Breuninger C, Dix S, Gerken T, Hunner M, Lehmann-Pape L, Hens K,
Jocher G, Kesselmeier J, Lüers J, Mayer JS, Moravek A, Plake D, Riederer M, Rütz F,
Scheibe M, Siebicke L, Sörgel M, Staudt K, Trebs I, Tsokankunku A, Welling M, Wolff
72
V Zhu Z (2012) Coupling processes and exchange of energy and reactive and nonreactive trace gases at a forest site – results of the EGER experiment. Atmos Chem Phys
12:1923-1950
Gao W, Li BL, (1993) Wavelet Analysis of Coherent Structures at the Atmosphere-Forest
Interface. J Appl Meteorol 32:1717-1725
Garstang M, Fitzjarrald DR (1999) Observations of Surface to Atmosphere Interactions in the
Tropics. Oxford University Press, New York, 405 pp
Garstang M, White S, Shugart HH, Halverson J (1998) Convective Cloud Downdrafts as the
Cause of Large Blowdowns in the Amazon Rainforest. Meteorol Atmos Phys 67:199212
Högström U, Bergström H (1996) Organized Turbulence in the Near-Neutral Atmospheric
Surface Layer. J Atmos Sci 53:2452-2464
Kaimal JC, Finnigan JJ (1994) Atmospheric Boundary Layer Flows. Their Structure and
Measurement. Oxford University Press, New York, 289 pp
Kruijt B, Malhi Y, Lloyd J, Nobre AD, Miranda AC, Pereira MGP, Culf A Grace J (2000)
Turbulence Statistics Above and Within Two Amazon Rain Forest Canopies. BoundaryLayer Meteorol 94: 297-331
Mafra ACB (2014) Características das trocas turbulentas noturnas de CO2 entre a floresta de
Uatumã, Amazonas, e a atmosfera. Master thesis, Universidade Federal do Pará, Brazil
Mahrt L (1998) Stratified Atmospheric Boundary Layers and Breakdown of Models. Theor
Comput Fluid Dyn 11: 263-279
Mahrt L (2007) The influence of nonstationarity on the turbulent flux-gradient relationship for
stable stratification. Boundary-Layer Meteorol 125:245-264
Mahrt L (2008) Mesoscale wind direction shifts in the stable boundary-layer. Tellus 60A:700705
Molion LCB (1987) Micrometeorology of an Amazonian Rain Forest. In: The Geophysiology
of Amazonia - Vegetation and Climate Interactions, Dickinson RE, Wiley-The United
Nations University, New York, pp 255-272
Nepstad D, Lefebvre P, d. Silva UL, Tomasella J, Schlesinger P, Solorzano L, Moutinho P,
Ray D, Benito JG (2004) Amazon drought and its implications for forest flammability
and tree growth - a basin-wide analysis. Global Change Biol 10:704-717
Panofsky HA, Dutton JA (1984) Atmospheric Turbulence. Wiley, New York, 397 pp
73
Paw U KT, Brunet Y, Collineau S, Shaw RH, Maitani T, Qiu J, Hipps L (1992) On coherent
structures in turbulence above and within agricultural plant canopies. Agric For
Meteorol 61:55-68
Poggi D, Porporato A, Ridolfi L, Albertson JD, Katul GG (2004) The effect of vegetation
density on canopy sub-layer turbulence. Boundary-Layer Meteorol 111:565-587
Poulos GS, Blumen W, Fritts DC, Lundquist JK, Sun J, Burns SP, Nappo C, Banta R,
Newsom R, Cuxart J, Terradellas E, Balsley B, Jensen M (2002) CASES-99: A
comprehensive investigation of the stable nocturnal boundary layer. Bull Am Meteorol
Soc 83, 4: 555-581
Raupach MR, Finnigan JJ, Brunet Y (1996) Coherent Eddies and Turbulence in Vegetation
Canopies: The Mixing-layer Analogy. Boundary-Layer Meteorol 78: 351-382
Robinson SK (1991) Coherent Motions in the Turbulent Boundary Layer. Annu Rev Fluid
Mech 23:601-639
Sá LDA, Pachêco VB (2006) Wind Velocity above and inside Amazonian Rain Forest in
Rondonia. Revista Brasileira de Meteorologia 21:50-58
Shuttleworth JW, Gash JHC, Lloyd CR, Moore CJ, Roberts J, Marques Filho AO, Fisch GF,
Silva Filho VP, Ribeiro MNG, Molion LCB, Sá LDA, Nobre CA, Cabral OMR, Patel
SR, Moraes JC (1985) Daily Variations of Temperature and Humidity within and above
Amazonian Forest. Weather, 40.4: 102-108
Silva Dias MAFS, Rutledge S, Kabat P, Silva Dias P, Nobre C, Fisch G, Dolman H, Zipser E,
Garstang M, Manzi A, Fuentes J, Rocha H, Marengo J, Plana-Fattori A, Sá LDA, Avalá
RCS, Andreae M, Artaxo P, Gielow R, Gatti L (2002) Clouds and rain processes in a
biosphere atmosphere interaction context in the Amazon Region. J Geophys Res D:
Atmos 1984–2012 107(D20), LBA-39
Starkenburg D, Fochesatto GJ, Prakash A, Cristóbal J, Gens R, Kane DL (2013) The role of
coherent flow structures in the sensible heat fluxes of an Alaskan boreal forest. J
Geophys Res D: Atmos 118:8140-8155
Steiner AL, Pressley SN, Botros A, Jones E, Chung SH, Edburg SL (2011) Analysis of
coherent structures and atmosphere-canopy coupling strength during the CABINEX
field campaign: implications for atmospheric chemistry. Atmos Chem Phys Discuss
11:21013-21054
Stull RB (1988) An Introduction to Boundary Layer Meteorology. Kluwer, Dordrecht, 666 pp
Sun J, Burns SP, Lenschow DH, Banta R, Newsom B, Coulter R, Frasier S, Ince T, Nappo C,
Cuxart J, Blumen W, Delany AC, Lee X, Hu XZ (2002) Intermittent Turbulence
74
Associated with a Density Current Passage in the Stable Boundary Layer. BoundaryLayer Meteorol 105:199-219
Sun J, Lenschow DH, Burns SP, Banta R, Newsom BK, Coulter R, Frasier S, Ince T, Nappo
C, Balsley BB, Jensen M, Mahrt L, Miller D, Skelly B (2004) Atmospheric
Disturbances that Generate Intermittent Turbulence in Nocturnal Boundary Layers.
Boundary-Layer Meteorol 110:255-279
Sun J, Mahrt L, Banta RM, Pichugina YL (2012) Turbulence Regimes and Turbulence
Intermittency in the Stable Boundary Layer during CASES-99. J Atmos Sci 69: 338-351
Thomas C, Foken T (2005) Detection of long-term coherent exchange over spruceforest using
wavelet analysis. Theor Appl Climatol 80:91-104
Thomas C, Foken T (2007) Flux contribution of coherent structures and its implications for
the exchange of energy and matter in a tall spruce canopy. Boundary-Layer Meteorol
123:317-337
Van de Wiel BJH, Moene AF, Hartogensis OK, De Bruin HAR, Holtslag AAM (2003)
Intermittent Turbulence in the Stable Boundary Layer over Land.Part III. A
Classification for Observations during CASES-99. J Atmos Sci 60:2509-2522
Vickers D, Göckede M, Law BE (2010) Uncertainty estimates for 1-hour averaged turbulence
fluxes of carbon dioxide, latent heat and sensible heat. Tellus B 62:87-99
Vickers D, Mahrt L (1997) Quality Control and Flux Sampling Problems for Tower and
Aircraft Data. J Atmos Oceanic Technol 14:512-526
Viswanadham Y, Molion LCB, Manzi AO, Sá LDA, Silva Filho VP, André RGB, Nogueira
JLM, Dos Santos RC (1990) Micrometeorological Measurements in Amazon Forest
during GTE/ABLE-2A Mission. J Geophys Res 95:13669-13682
Von Randow C, Sá LDA, Prasad GSSD, Manzi AO, Arlino PRA, Kruijt B (2002) Scale
Variability of Atmospheric Surface Layer Fluxes of Energy and Carbon over a Tropical
Rain Forest in Southwest Amazonia. I. Diurnal Conditions. J Geophys Res D: Atmos
107:D20 8062
von Randow C, Zeri M, Restrepo-Coupe N, Muza M. N, Gonçalves LGG, Costa MH, Araújo
AC, Manzi AO, Rocha HR, Saleska SR, Alaf Arain M, Baker IT, Cestaro BP,
Christoffersen B, Ciais P, Fisher JB, Galbraith D, Guan X, van der Hurk B, Ichii K,
Imbuzeiro H, Jain A, Levine N, Miguez-Macho G, Poulter B, Roberti DR, Sahoo A,
Schaefer K, Shi M, Tian H, Verbeeck H Yang Z.-L (2013) Inter-annual variability of
carbon and water fluxes in Amazonian forest, Cerrado and pasture sites, as simulated by
terrestrial biosphere models. Agric For Meteorol 182-183:145-155
75
Zeri M, Sá LDA (2011) Horizontal and Vertical Turbulent Fluxes Forced by a Gravity Wave
Event in the Nocturnal Atmospheric Surface Layer over the Amazon Forest. BoundaryLayer Meteorol 138:413-431
Zeri M, Sá LDA, Manzi AO, Araújo AC, Aguiar RG, von Randow C, Sampaio G, Cardoso
FL, Nobre CA (2014) Variability of Carbon and Water Fluxes Following Climate
Extremes over a Tropical Forest in Southwestern Amazonia. PLoS One 9. 2: e88130
Zeri M, Sá LDA, Nobre CA (2013) Estimating Buoyancy Heat Flux Using the Surface
Renewal Technique over Four Amazonian Forest Sites in Brazil. Boundary-Layer
Meteorol 149:179-196
76
Capítulo 4
__________________________________________________
Dias-Junior, C.Q. Marques Filho, E.P. Sá,
L.D.A. 2015. LES applied to analyze the
turbulent flow organization above amazon
forest. Submetido para Journal of Wind
Engineering and Industrial Aerodynamics.
77
LES applied to analyze the turbulent flow organization above amazon
forest
Cleo Q. Dias-Junior1,2; Edson P. Marques Filho3; Leonardo D. A. Sá4.
1 - Federal Institute of Education Science and Technology of Pará/Bragança, Brazil
2 - National Institute of Amazonian Research / CLIAMB, Manaus, Brazil
3 - Federal University of Bahia, Salvador, Brazil
4 - National Institute for Space Research/CRA, Belém, Brazil
Corresponding author: [email protected]
Abstract The occurrence of coherent structures (CSs) above the Amazon forest is analyzed.
To perform this study, Large Eddy Simulation is used, which has been improved by the
introduction of a drag force which is representative of a typical Amazon forest canopy. The
simulation’s results show that the flow is sensitive to the presence of canopy and an inflexion
point is simulated in wind profiles. In addition, the profiles of momentum flux and turbulent
kinetic energy are similar to those obtained experimentally. On the region between 1h and 4h
several CSs features associated with turbulent flow regarding pressure, momentum fluxes,
skewness and vorticity fields are detected suggesting that “roll” structures arranged
perpendicularly to the mean wind direction populate this region. It is interesting to mention
that: i) the skewness of the wind velocity has also a maximum value on the region, what
indicates an asymmetric distribution of the wind velocity relatively to its mean value, fact that
might be associated to the generation process of the “roll” structures; ii) the horizontal
vorticity component transversal to the mean wind direction is greater than the vorticity
components on the other orthogonal directions suggesting that “roll” structures move
perpendicularly to the mean wind direction.
Keywords: LES; Rougness sublayer; Reynolds stress; Coherent strucuture; Amazon forest.
1. Introduction
It is well known that forests play an important role in the mass, energy and momentum
exchange processes between vegetation and the atmosphere (Fitzjarrald et al., 1990; Kruijt et
al., 2000; von Randow et al., 2004). Tropical forests, such as the Amazonian, require special
attention, since are characterized by an energy balance at the forest canopy in which the latent
heat fluxes are greater than the sensible heat fluxes, with very low values of the Bowen ratio
78
(in general, less than 0.4), what strongly contributes to the warming of the tropical
troposphere (Silva Dias et al., 2002;. von Randow et al., 2002; Betts et al., 2009).
Furthermore, the availability of water for evaporation processes directly affects several
feedback processes spanning clouds generation, turbulent transport, radiative exchanges,
hydrological processes and ecophysiological issues (Betts, 2004; Betts et al., 2009; RestrepoCoupe et al., 2013; Zeri et al., 2014). In recent decades many researchers performed a lot of
effort for a better understanding of exchanges between the Amazon forest and the atmosphere,
particularly the turbulent processes (Fitzjarrald et al., 1990; Kuijt et al., 2000; Silva Dias et al,
2002; von Randow et al, 2002; Zeri and Sá, 2011; Dias-Junior et al., 2013; Zeri et al., 2014).
With
this
objective,
large
experimental
projects
such
as
Amazonian
Region
Micrometeorological Experiment (ARME), Global Troposphere experiments/Amazon
Boundary Layer Experiment (GTE-ABLE), Brazilian Amazonian Climate Observation Study
(ABRACOS), The large-scale Biosphere-Atmosphere Experiment in Amazonia (LBA) were
carried out in order to have a more systematic view of the processes that occur in the Amazon
forest's environment. One of the latest, LBA, was a multinational and interdisciplinary
research program, whose main objective was to better understand climatological, ecological,
biogeochemical and hydrological issues of Amazonia, as a regional entity, in a scenario with
perspective of global climate change (Avissar and Nobre, 2002).
However, studies with experimental data still present certain restrictions, such as: i)
difficulties in accurately determining the height of the rough sublayer and its diurnal and
seasonal variability; ii) understand the aspects of the turbulence structure at different heights
above the canopy, particularly as regards the characteristics of the existing eddies within the
inner, outer and transition layers (McNaughton and Laubach, 2000; Malhi et al., 2004) and
what are the possible relationships they have among themselves; iii) the difficulty in
understanding why, under certain conditions, there may be cases involving active turbulence
or non-active turbulence (Högström, 1990).
An alternative to overcome this problem is through the use of Large Eddy Simulation
(LES), a three-dimensional modeling procedure which: i) directly resolved the major
turbulent flow structures, which contain most of the flow energy and occurs at the
atmospheric boundary layer larger scales; ii) is intended for parameterize only the smallest
turbulent structures, generally associated with the inertial subdomain region of the turbulence
spectrum (Sagaut et al., 2006). LES is based on the assumption that the flow's structures in the
smaller scales, such as those in the inertial subrange of developed turbulence, tend to be more
homogeneous and isotropic and therefore less affected by the actual boundary conditions
79
(Smagorinsky, 1984). Thus, it can be expected that the modeling with respect to these scales
have a universal character, i.e., less dependency on the type of flow being simulated
(Maruyama et al., 1999; Pope, 2004).
Few studies using LES have been published in the international literature concerning
the Amazon region. Among the few can be mentioned da Silva et al. (2011) who used the
LES to investigate the role of latent heat flux and the consequent formation of clouds above a
fluvial bay in the eastern Amazon and Vilà‐Guerau de Arellano et al. (2011) who investigated
the diurnal variability of the concentration of some chemical species in the Amazon region.
However, practically have not studies that used LES to characterize the organization of the
turbulent flow above the Amazon forest in order to obtain suitable information regarding
some features of the turbulent flow within the roughness sublayer above the vegetation.
This work started with the entering a vertical profile of the leaf area index (LAI) into
the LES model. This in order to validate the LES simulations against available experimental
data of the LBA’s “Rebio Jarú” reserve, in western Amazon, and also to obtain a better
understanding of the organization of turbulence, its statistical moments, wind velocity and
vorticity fields and vertical variability above and within the forest environment. In addition,
CSs, in its sweep and ejection phases, are investigated for predominantly neutral conditions.
In general the wind velocity fields generated by LES agree quite well with the available
experimental data.
2. Experimental data
First a brief description will be made of Rebio Jarú forest reserve, since some of the
parameters that were entered in the model (sensible heat flux, latent heat flux, the virtual
potential temperature, specific humidity, height of the boundary layer, the Coriolis parameter)
are experimental data collected there. This was performed to enter these parameters in order
to make the simulations as realistic as possible.
The Jarú forest reserve (Rebio Jarú), located southwest of the Amazon, has an area of
approximately 268,150 hectares between 10005'S and 10019'S and 61035'W and 61o57'W,
with altitude ranging from 100 m to 150 m above sea level. For more information on its
climatology see Dias-Junior. et al. (2013). According Andreae et al. (2002) this forest reserve
is characterized by area of native vegetation of tropical forest with an average height ranging
between 30 m and 35 m, with some species reaching up to 45 m high. Marques Filho et al.
(2005) reported LAI equal to 5.0 in the reserve. Fig. 1 shows the 60 m height aluminum
80
micrometeorlogical tower (1004.706'S and 61056.027'W) which was provided with
micrometeorological instruments, whose descriptions can be found in Zeri and Sá (2010).
Fig. 1. Picture showing the meteorological tower built at Rebio Jarú forest reserve and the surrounding
vegetation.
3 Numerical methods
In this work we used the LES code originally developed by Moeng (1984) and
modified by Moeng and Sullivan (1994). We simulated the turbulent flow within and above
the Amazon forest. For this work be presented in a didactic way we will perform some basic
descriptions of the LES's version used here and the modifications contained therein.
3.1. Numerical implementation
In LES models the separation between the solved scale and the subgrade one is
obtained by applying a low-pass filter on the variables of the Navier-Stokes (N-S) equations
(Eq 1, 2 and 3) for an incompressible fluid (Leonard, 1974; Sagaut et al., 2006, pp. 31). Thus,
the variables filtered correspond to a volumetric average and describe the turbulent motions in
the solved scale (Deardorff, 1972). Scales not explicitly solved by LES are parameterized. In
81
this work we shall use the symbols 𝑥̅ and 𝑥 ′′ to represent a variable x in any solved scale and
subgride, respectively.
̅
𝜕𝑢
𝜕𝑡
𝜕𝑣̅
𝜕𝑡
̅
𝜕𝑤
𝜕𝑡
= ̅̅̅̅̅
𝑢̅𝜉̅𝑧 − ̅̅̅̅̅
𝑤
̅𝜉̅̅̅
𝑦 + 𝑓𝑣̅ −
𝜕𝑃 ∗
̅̅̅̅̅
= ̅̅̅̅̅
𝑤
̅𝜉̅𝑥 − 𝑣̅
𝜉̅𝑧 + 𝑓𝑢̅ −
𝜕𝑃 ∗
̅
̅̅̅̅̅
̅̅̅̅̅
̅ 𝑔𝜃
= 𝑢
̅𝜉̅̅̅
𝑦 − 𝑣̅ 𝜉𝑧 + 𝜃 −
𝜕𝑃 ∗
0
𝜕𝑥
𝜕𝑦
𝜕𝑧
−
−
−
𝜕〈𝑃̅〉
𝜕𝑥
𝜕〈𝑃̅ 〉
𝜕𝑦
𝜕𝜏𝑥𝑧
𝜕𝑥
−
−
−
𝜕𝜏𝑥𝑥
𝜕𝑥
𝜕𝜏𝑥𝑦
𝜕𝑥
𝜕𝜏𝑦𝑧
𝜕𝑦
−
−
−
𝜕𝜏𝑥𝑦
𝜕𝑦
𝜕𝜏𝑦𝑦
𝜕𝑦
𝜕𝜏𝑧𝑧
𝜕𝑧
−
−
𝜕𝜏𝑥𝑧
𝜕𝑧
𝜕𝜏𝑦𝑧
𝜕𝑧
̅
𝜕𝑤
− 〈 𝜕𝑡 〉
(1)
(2)
(3)
Here brackets denote horizontal averages 𝜉𝑥 , 𝜉𝑦 , 𝜉𝑧 are the vorticity components in x, y
and z, respectively. 𝜌0 is the mass density of air, P is the grid average pressure, g is the
gravitational acceleration. 𝜏𝑖𝑗 are the subgrid-scale Reynolds stresses. 𝜃 is the potential
temperature, and 𝜃0 is the reference potential temperature (304 K in our simulations)
The equations of motion are solved numerically using a pseudoespectral method in
horizontal directions and finite difference scheme of second order centered in space in the
vertical direction. The temporal derivatives are discretized using the 2nd order AdamsBashforth scheme, stable for small time steps (Mesinger and Arakawa, 1982). The numerical
stability of the system is determined by calculating the number of Courant in each time step
(∆𝑡) (Courant et al., 1967). The lateral boundary conditions are assumed to be cyclic. The
Monin-Obukhov similarity theory is used to estimate the momentum turbulent fluxes on the
surface. This boundary is considered rigid, and with zero vertical velocity. The upper
boundary condition is radiative, with zero vertical gradients for the horizontal components of
wind speed and subgrid turbulent fluxes. For consistency, in LES model the vertical velocity
is also zero at the grid top.
A numerical grid of 128 x 128 x 256 points distributed in an equally spaced way over
an area of 2 x 2 Km2 in the horizontal plane and up to 1 Km in the vertical direction was used,
resulting in cells of 15.62 m on the horizontal direction and 3.9 m on the vertical direction.
This resolution is large enough to capture numerous surface flow structures which often have
length scales of the order of the canopy height on the horizontal direction, and of the order of
one third of the canopy height on the vertical direction (Raupach et al., 1996; Finnigan, 2000).
It is important to mention that LES relies on directly resolving the large scales of
turbulent motion. Furthermore subgrid scales have a little contribution to the total turbulent
82
momentum flux and energy (Edburg et al., 2012). For this reason in this present simulation
we used only resolved scales.
3.2. Canopy structure
The drag imposed by the forest canopy upon the atmospheric flow was introduced in
the model by an additional force in the N-S equations. Such a force is expressed by the
product of the drag coefficient (𝑐𝑑 ), the leaf area density (LAD) and the square of the
instantaneous velocity, as proposed by Patton et al. (2003). The drag force generated by the
canopy (𝐹̅ ) is three-dimensional and time-dependent and can be written as follows (Shaw and
Schumann, 1992; Patton et al., 2003; Dupont and Brunet, 2009):
̅ = −𝑐𝑑 𝐿𝐴𝐷|𝒖
̅ |𝒖
̅
𝑭
(4)
̅ | is the current resolved scalar wind speed and 𝒖
̅ is the resolved velocity vector
where |𝒖
̅, 𝒗
̅, 𝒘
(𝒖
̅ ) in the (x, y, z) directions, where x refers to the downstream, y to the spanwise an z to
the upward directions. Since the goal is to simulate the turbulent flow above the Rebio Jarú is
important to use some parameters that incorporate the roughness of the Amazon forest into
the model. Given that some researchers found parameters such as: i) LAI equal to 5.0,
obtained by Marques Filho et al. (2005); ii) the average canopy height (h) equal to 35 m as
mentioned by Andreae et al. (2002). These parameters were introduced into the LES model.
In addition, was used LAD similar to that found by Marques Filho et al. (2005) in order to
allow simulations to reproduce the turbulent flow in the Rebio Jarú forest reserve the most
realistic way possible. Fig. 2 shows the vertical profile of the LAD encountered by Marques
Filho et al. (2005) for the Rebio Jarú (gray area) and introduced into LES in this study (black
line).
83
Fig. 2. Vertical Profile of leaf area density of the Rebio Jarú forest reserve (for LAI = 5.0): Found by Marques
Filho et at. (2005) (gray region) and modifications inserted in the LES used in this work (black line).
3.3. Initial and boundary conditions
The initial objective of this study is to simulate the turbulent flow above and within
the forest canopy for approximately neutral conditions (h/L = -0.15, where L is the Obukhov
length). Therefore, the initial and boundary conditions, as well as external forcing, were
chosen so as to generate a planetary boundary layer corresponding to an early morning
convective period of (between 09 H and 10 H, local time). At this time the sensible heat flux
is still low and the conditions of stability are still approaching to neutrality. Therefore, we
used experimental data corresponding to the local time between 09 H and 10 H, for the Julian
days between 40-45 of 1999. These data were entered into the model as initial condition
(Table 1).
Table 1. simulations parameters and bulk statistics
Mean horizontal wind
speed (U)
heat flux (Q)
Coriolis parameter (f)
Drag coeficiente (𝒄𝒅 )
Inversion height (𝒛𝒊 )
Obukhov length, (L)
Friction velocity (𝒖∗ )
3.5 𝒎/𝒔
0.05 𝐾/𝑠
- 2.55 𝑥 10−5 𝑠 −1
0.30
500 m
- 227 m
0.52 m/s
The initial vertical profiles of horizontal components of wind speed are assumed to be
equal to the values of the components of the geostrophic wind (Fig. 3c). The initial vertical
profiles of potential temperature and water vapor were established to play a mixed layer (ML)
role with a potential temperature of 304 K (Fig. 3a) and specific humidity of 20 g/kg (Fig.
3b). This has been done in order to enter the humidity's buoyancy into the model, as a part of
the virtual potential temperature 𝜃𝑣 (Stull, 1988, pp 275). These values are averages obtained
with the experimental data. The depth of the ML was 500 m (Garstang and Fitzjarrald, 1999;
Oliveira and Fisch, 2000). In the heat exchange in the ML, the 𝜃𝑣 value ranges from 3 K
along a vertical length of 24 m (6 grid points) (Oliveira and Fisch, 2000). In the free
atmosphere above the inversion layer, 𝜃𝑣 varies at a rate of approximately 4 K/ Km (Garstang
and Fitzjarrald, 1999, pp. 261).
84
a)
b)
c)
Fig. 3. Vertical profiles of (a) virtual potential temperature (𝜃𝑣 ); (b) specific humidity (q); (c) horizontal velocity
components; used as initial condition in the LES.
4. Results
This paper aims to characterize the turbulent flow at the interface Amazon rainforestatmosphere. For this, statistical moments of first, second and third order were calculated from
the vertical profiles of wind speed found as results of LES modeling. These profiles
correspond to the horizontally averaged statistics of the resolved flow field (streamwise and
spanwise) for a given z (vertical location) as performed by Shen and Leclerc, 1997. 10,000
time steps (Δt) for all runs have been integrated, and the 4,000 initial Δt were needed to arrive
at a computational equilibrium. Thus, temporal statistical analyzes were carried out based on
the average field generated by LES after initial 4000 Δt, that is, when the turbulent fields
exhibited a near-equilibrium condition. The mean fields were saved every 2000 Δt. It should
be noted that throughout the simulation, a time step of 1s was kept fixed.
4.1. Mean statistical fields above the Amazon rainforest
Initially some vertical profiles of simulated variables are analyzed for: i) wind speed;
ii) turbulent kinetic energy (TKE); iii) momentum flux; and iv) standard deviation of u and w.
This is performed in order to compare our findings with those of other studies, both
experimental as modeling ones, which also analyzed the turbulent flow over rough surfaces,
like forests. This comparison is important as it will assess the ability of the LES model used in
this work in simulating the turbulent flow over a forest with LAD similar to that found in the
Amazonian rainforest.
85
Figs. 4a and 4b show vertical sections of the horizontal wind speed (𝑈 = [𝑢2 +
𝑣 2 ]1/2 ) and of the TKE, respectively, both being normalized with the friction velocity, 𝑢∗ ,
calculated at canopy top. Observing Fig. 3a, is detectable an inflection point on the vertical
wind profile next the top of the canopy. This result is similar to those already obtained both
experimentally above the Amazon rainforest (Sá and Pacheco 2006; Dias-Junior et al., 2013;
de Souza et al., 2015) and in other forested regions (Raupach et al., 1996; Finnigan, 2000) as
well as to the ones provided by LES modeling regarding several experimental fields (Shaw
and Schumann, 1992; Patton et al. 2003; Finnigan et al., 2009; Edburg et al., 2012; Schlegel
et al., 2014; and others) and also by wind tunnel experiments (Raupach, 1981; Marshall et al.,
2002).
By observing the TKE profile of Fig. 4b it is possible to note that the turbulent energy
is maximum near the top of the tree canopy and its value falls down rapidly within the forest
canopy. This occurs as a consequence the action of the drag force imposed by the forest
canopy (Raupach and Thom 1981; Meyers and Baldocchi, 1990; Shen and Leclerc, 1996;
Dupont and Brunet, 2009). Above the vegetation is observed that TKE shows a gradual
decay. Experimental studies (Shaw et al., 1988; Su et al., 1998) and modeling (Shen and
Leclerc, 1996; Su et al., 1998; Dupont and Brunet, 2009; Edburg et al., 2012) also showed
that TKE decreases rapidly inside the canopy, changing slowly or remaining constant above
the treetops as obtained by LES simulation.
a)
b)
Fig. 4. Vertical profile: a) of horizontal wind speed and b) of turbulent kinetic energy. Both normalized by the
fiction velocity calculated at canopy top.
Fig. 5a shows the vertical profiles of the standard deviations of u and w (σu and σw,
respectively). It could be observed that both σu and σw, decrease with the decline of the
86
measurement height. However, above the trees σw practically does not change value, while σu
decreases slightly with the height. Incidentally, Fitzjarrald et al. (1990) analyzed data from the
Duke forest reserve, located in the central Amazon. They used three different measurement
heights; one within the canopy (0.67 h) and the other two above the canopy (1.12 h and 1.27
h). They showed that the σw values presented gentle variations above the canopy. However,
within the vegetation, they observed that the σw value fell by half, compared with values
above the canopy. Besides, Su et al. (1998) used data from a deciduous forest located in
Canada with LAI equal to 2. For this forest they found a profile 𝜎𝑢 /𝑢∗ similar to the one
obtained with our LES modeling. Several other studies have used the LES (Patton et al., 2003;
Finnigan et al., 2009; Edburg et al., 2012) or wind tunnel (Raupach, 1981; Brunet et al., 1994;
Marshall et al., 2002) to investigate the vertical profile of the behavior of 𝜎𝑢 /𝑢∗ and 𝜎𝑤 /𝑢∗ .
The results in these other works closely approximate the results found here.
Fig. 5b shows the vertical profile of the normalized momentum flux < 𝑤 ′ 𝑢′ >/𝑢∗2 .
Note that there is a rapid decrease of 〈𝑤 ′ 𝑢′ 〉/𝑢∗2 with depth inside the canopy. On the other
hand, above the forest canopy 〈𝑤 ′ 𝑢′ 〉/𝑢∗2 is practically constant. Is convenient to mention that
Raupach et al. (1996) in their investigation about momentum absorption by several kind of
vegetation canopies also noted that above the canopy 〈𝑤 ′ 𝑢′ 〉/𝑢∗2 is approximately constant
with height, but declines rapidly within the crown's vegetation.
As observed by Raupach et al. (1996) 〈𝑤 ′ 𝑢′ 〉/𝑢∗2 tends to zero close to the ground,
indicating that almost all the horizontal momentum was absorbed by the canopy.
Other studies using the LES to model the turbulent flow over forests, also reached
similar results for 〈𝑤 ′ 𝑢′ 〉/𝑢∗2 (Su et al., 1998; Patton et al., 2003). Nevertheless some results
with LES investigation suggest that 〈𝑤 ′ 𝑢′ 〉/𝑢∗2 is practically zero from the half of the canopy
down (Finnigan et al., 2009; Edburg et al., 2012). However, these results were found for
simulations where the LAI was less than 5.0, in which possibly the momentum flux between
the regions above and within the forest canopy is quite different from that of the terra firme
Amazonian forest, which is the goal of this investigation.
87
a)
b)
Fig. 5. Vertical profile: a) standard deviation of the streamwise velocity (dashed line) and standard deviation of
the vertical velocity (solid line) and b) of momentum flux. Both normalized by the fiction velocity calculated at
canopy top.
Based on the vertical profiles of U, TKE, 𝜎𝑢 , 𝜎𝑤 e 〈𝑤 ′ 𝑢′ 〉 it is possible to suggest that
the turbulent flow above a vegetated surface with characteristics similar to the Amazon
rainforest’s ones, is being simulated quite well. As a next step, other profiles are analyzed,
such as: i) sweep and ejection phases of CSs; ii) the correlation coefficient between the
horizontal and vertical wind speed (𝑟𝑤𝑢 ); iii) skewness of the horizontal (𝑆𝑘𝑢 ) and vertical
(𝑆𝑘𝑤 ) components of wind velocity; iv) standard deviation of pressure; v) vorticity field.
Proceeding in such way is possible to obtain a more accurate picture of the turbulent flow
organization over extremely rough surfaces, such as the Amazonian rainforest.
4.2. Sweeps and ejections.
It is expected that the momentum flux near the surface is negative, as momentum is
always being transported downwards in order to be dissipated by friction in the regions closer
to the surface. However, this negative value of momentum flux is associated with two
physically quite different conditions, depending on the step of the CS’s cycle above the
canopy, namely: i) 𝑢′ > 0 and 𝑤 ′ < 0; ii) 𝑢′ < 0 and 𝑤 ′ > 0. In the first case, a flow’s parcel
with positive fluctuation of momentum is brought down into the canopy, and the second case,
a flow’s parcel with u-momentum's deficit is transferred upwards from the canopy.
Momentum flux 〈𝑤 ′ 𝑢′ 〉 can be partitioned into four associated quadrants in
accordance with the signs of w' and u' (Raupach, 1981; Shaw et al., 1983). Several results
from experimental data and from LES modeling have shown that the contributions from
88
ejections (quadrant 2: 𝑤 ′ > 0 and 𝑢′ <0) and sweeps (quadrant 4: 𝑤 ′ < 0 and 𝑢′ > 0) are the
major constituents of the momentum fluxes, both above and within forest canopies (Raupach,
1981; Baldocchi and Meyers, 1988; Kanda and Hino, 1994; Finnigan, 2000; Dupont and
Brunet, 2009; Finnigan et al., 2009; Dupont and Patton, 2012). In this work the sum of the
sweep and ejection contributions for momentum fluxes corresponds approximately to 74%
and 65% of the total flux above and within the canopy, respectively (not shown).
Fig. 6 shows the vertical profile of the ratio 𝑅 = 〈𝑤 ′ 𝑢′ 〉4 /〈𝑤 ′ 𝑢′ 〉2 between
momentum flux for the sweep and ejection phases. It can be observed that within the
vegetation, the sweeps contribute more significantly for 〈𝑤 ′ 𝑢′ 〉 than the ejections. A
maximum R value is observed at the level z ≈ 0.7 h (Sign I on the figure). According to Silva
Dias et al. (2002), in the Rebio Jarú reserve this level approximately coincides with the zeroplane displacement height (d), the mean level of momentum absorption within the canopy
(Jackson, 1981). Besides, Shen and Leclerc (1997) based on their LES results found that
approximately at this z ≈ 0.7 h level the pressure forces present its maximum intensity within
canopy.
The situation above the canopy is exactly the opposite, i.e. ejections are more
important than sweeps for the total flux of momentum. R depicts a minimum value, slightly
less than 0.5, at the height z ≈ 3h (Sign II on the figure), and from this point upwards the value
R decreases with height. It can also be noted that in the treetop (z = h) the ejections and
sweeps occur in approximately equal proportions.
Several experimental and simulation results have shown that sweep's intensity exceeds
ejection's intensity within the vegetation (Raupach, 1981; Baldocchi and Meyers, 1988; Gao
et al., 1989; Kanda and Hino, 1994; Shen and Leclerc, 1997; Su et al., 1998; Launiainen et al.,
2007; Poggi and Katul, 2007; Dupont et al., 2008). However, in the forest-atmosphere
interface and above the canopy there is some divergence between the results found in the
literature. Several researchers, using experimental and LES data, found results similar to those
obtained here, i.e. sweeps and ejections occur in approximately equal intensities in the forestatmosphere interface. According with our results, from the treetop upwards the ejections start
to dominate the total flux of momentum (Baldocchi and Meyers, 1988; Lee and Black, 1993a;
Shen and Leclerc, 1997; Katul and Albertson, 1998; Su et al., 1998; Launiainen et al., 2007).
However, other results showed that, at canopy top, the sweeps are primarily responsible for
the generation of momentum flux (Raupach and Thom, 1981; Gao et al., 1989; Kanda and
Hino, 1994; Poggi and Katul, 2007; Dupont et al., 2008).
89
Fig. 6. Flux ratio: momentum flux by sweep ( 𝑤 ′ < 0 𝑒 𝑢′ > 0) to that by ejection (𝑤 ′ > 0 𝑒 𝑢 ′ < 0).
4.3. Efficiency of momentum transport.
An interesting feature of turbulent flow near the ground surface is that TKE generated
near the inferior boundary is not always fully used to generate turbulent flux, that is, for the
′2 , v
′2 and w
′2 may be generated distinct values of ̅̅̅̅̅̅
′ w ′ , depending
̅̅̅̅
̅̅̅̅
̅̅̅̅̅
̅̅̅̅̅̅
same values of u
u′ w ′ e v
on specific environmental conditions (Högström, 1990; Katul et al., 1996). The understanding
the causes of these differences provides information for a better understanding of the genesis
of the turbulence structure near the surface.
The correlation coefficient 𝑟𝑤𝑢 = 〈𝑤 ′ 𝑢′ 〉/𝜎𝑤 𝜎𝑢 might be interpreted as a measure of
the efficiency of the turbulent field be able to generate turbulent flux. In order to illustrate this
proposition, we present the Fig. 7, in which 𝑟𝑤𝑢 is plotted as a function of the normalized
height. It is observed that 𝑟𝑤𝑢 decreased dramatically downward into the canopy (starting
from sign I). In the region between 1 h and 4 h (between the signs I and II) 𝑟𝑤𝑢 practically
does not change its value (𝑟𝑤𝑢 varies between 0.42 and 0.43). Similar results was found by
Raupach et al. (1996), using data from wind tunnel and from different vegetation cover,
shown that immediately above the canopy 𝑟𝑤𝑢 has values around -0.5 with its intensity
decreasing downward. Researchers such as Launiainen et al. (2007), using data from a pine
forest located in Finland, showed that 𝑟𝑤𝑢 has maximum intensity near the top of the canopy
(𝑟𝑤𝑢 ranging between -0.4 and -0.5). Results applying LES above forest canopies also
corroborate the results found here (Su et al., 1998; Dupont and Brunet, 2009). This reinforces
90
the conviction that our LES modeling results agree quite well with the main results presented
in the literature.
Fig. 7. Vertical profile of correlation coeficiente between u e w (𝑟𝑤𝑢 ).
4.4 Moments of third order for the wind speed.
(𝑆𝑘𝑢 ) and (𝑆𝑘𝑤 ), respectively, the skewnesses of u and w, are related to the degree of
asymmetry of the probability distribution of u and w around their respective average values.
The values of these parameters provide useful information about some features of momentum
vertical transport in the forest-atmosphere interface in its various steps. Non-zero values of
(𝑆𝑘𝑢 ) and (𝑆𝑘𝑤 ) are typical manifestations of the existence of heterogeneous turbulence
(Lumley and Panofsky, 1964, pp. 94), since under turbulent conditions homogenous expected
that the velocity distribution is Gaussian, with equal skewness to zero and kurtosis equal to 3
(Sorbjan, 1989, pp.41). Skewed processes are fundamental for the consolidation of an
inhomogeneous turbulent field at the forest environment, even in the situations in which the
roughness elements introduced in the simulation are horizontally homogeneous (as in the case
of this simulation). Fig. 8 shows the vertical profile of 𝑆𝑘𝑢 and 𝑆𝑘𝑤 simulated for Rebio Jarú.
It is possible to see that: i) in the forest-atmosphere interface (sign I) 𝑆𝑘𝑢 and 𝑆𝑘𝑤 show
values close to zero; ii) Within the canopy 𝑆𝑘𝑢 is positive and 𝑆𝑘𝑤 is negative, as found also
by several other researchers using experimental data (Baldocchi and Meyers, 1988a; Katul
and Albertson, 1998; Su et al., 1998; Katul and Chang, 1999; Finnigan, 2000; 2000;
Launiainen et al., 2007). According to Poggi and Katul (2004) there is a general trend of 𝑆𝑘𝑢
be positive and 𝑆𝑘𝑤 be negative within the canopy, which according to Baldocchi and Meyers
91
(1988) can be attributed to the greater intensity of turbulence at the canopy top, which is
carried down by the negative fluctuations of w'. Poggi and Katul (2004) point out that in
denser canopies there is a predominance of sweeps comparatively to ejections. This tendency
will reflect on the signs of the skewnesses of u and w. iii) Above the forest canopy 𝑆𝑘𝑢 < 0
and 𝑆𝑘𝑤 > 0 and they change sign at the level z/h = 1, which corresponds to the mean tree
height. From this level downwards 𝑆𝑘𝑢 becomes negative and 𝑆𝑘𝑤 becomes positive, what
should be explained by the third order momentum budget at the Amazonian forest-atmosphere
interface discussed by Fitzjarrald et al. (1990). Poggi and Katul (2004) point out those
changes in sign of 𝑆𝑘𝑢 and 𝑆𝑘𝑤 , above the canopy, may be related to the fact that ejections
dominate the turbulent changes of momentum there, as found in this simulation
It is important to mention that Fitzjarrald et al. (1990) are among the first researchers
which used experimental data to calculate the 𝑆𝑘𝑤 above and within the Amazonian forest
(Ducke Reserve, in central Amazonia). They showed that 𝑆𝑘𝑤 is positive above the canopy
and becomes negative within the forest canopy during the day. At the canopy top 𝑆𝑘𝑤 tends to
zero. This findings corroborate the results presented here and those of other authors (Kruijt et
al., 2000; Poggi and Katul, 2004; Dupont and Brunet, 2009).
Another interesting issue to be mentioned refers to the difference in the values of 𝑆𝑘𝑢
and 𝑆𝑘𝑤 as calculated on regions with distinct LAI values (Su et al., 1998; Katul and Poggi,
2004; Dupont and Brunet, 2009). According to Poggi and Katul (2004) these differences in
the skewness values are a consequence of the fact that within canopies with greater LAI,
sweeps and ejections are the main agents responsible for the generation of momentum flux
within and above the canopy, respectively, as mentioned above. However, for less dense
canopies, sweeps and ejections play similar roles concerning flux production.
92
Fig. 8. Vertical profiles of skewness of u (dotted line) and w (solid line).
4.5. Standard deviation of pressure.
To start the analysis of the pressure in turbulent fields, it is important to take into
account that the pressure action at a given point of the flow derives not only from local
forcings, but depends on the integrated effect of velocity and temperature fields as a whole
(Townsend, 1976, pp 43-44). According to the authors the pressure fluctuation in a turbulent
flow results from the combined action of three main factors: i) the interaction between the
mean velocity gradients and turbulent fluctuation gradients; ii)
the fluctuations in the
Reynolds stress acting on its average value; iii) the influence of buoyancy forces in inducing
pressure fluctuations in the flow.
Obtaining of pressure fluctuations measurements in turbulent field is not an easely
performed task, especially on works using experimental data, even the pressure fluctuation
forces playing a very important role in the turbulent processes, particularly with regard to the
return to isotropy term (Townsend, 1976, pp 165-166; Stull, 1988, pp 123). However,
pressure fluctuations profiles are often used in work such as wind tunnel and LES (Su et al.,
1998; Shen and Leclerc, 1997; Dupont and Brunet, 2009; Finnigan et al., 2009).
In this research the vertical profile of σp normalized by 𝑢∗ , is showed in Fig. 9. It is
possible to observe that σp decreased from the canopy top downward to the ground. From the
canopy top upwards, σp increases until approximately 2.5 h (sign II); above 2.5 h σp
practically does not change value reflecting the fact that at this level, the individual non
homogeneities of the turbulent flow generated near the canopy top are no more capable to
93
influence the pressure field of the turbulence heterogeneous bottom boundary, with its impact
objects and turbulent wakes (Griffin, 1981).
Another interesting feature of σp is that it presents an inflection point near the canopy
top (sing I), almost at the same height in which an inflection point was detected on the wind
profile, which seems to support the assumption of Raupach et al. (1996) regarding the
existence of two superimposed layers in this region and the consequent presence of a like
“mixing - layer” organization of the turbulence there.
Fig. 9. Vertical profile of standard deviation of pressure normalized by 𝑢∗ .
4.6. Vorticity.
Turbulent flows are essentially rotational since they present zones with considerable
vorticity in a wide range of scales, which is expressed by the existence of vortex (regions in
which the vorticity is concentrated) in a wide range of sizes (Abry, 1997, pp. 220). The
vorticity at each point of the flow is defined as 𝝎 = 1/2 (𝛁 𝑥 𝒖) (Feynman et al., 1964, Chap
40.5; Frisch, 1995, pp. 16). Authors such as Gerz et al. (1994) discussed the importance of the
existence of a vorticity field in turbulent flow and its ability to generate CSs and vortex tubes,
which can be better understood by analyzing the terms of the tendency of vorticity equation
(Tennekes, 1985), particularly its term ωj (∂ui/∂xj) entitled “stretching” and “twisting”, where
ui is the velocity fluctuation in the i-direction, and (∂ui/∂xj) is the gradient ui in the j-direction
(Aris, 1990, pp.88).
Thus, the vorticity field arranged in vortex tubes evolves over time in such way that
the regions with high concentration of ωj are stretched in the direction j and compressed in
other directions, and ωj may also have its rotation axis direction modified by the action of the
94
twisting term (Gerz et al., 1994; Abry, 1997, pp 221). According to these authors, this process
is indirectly associated with a tendency of larger structures give rise to smaller ones.
It is important to note that the calculation of vorticity from experimental data, it is not
a trivial task, since to carry out such procedure would request an experimental design quite
sophisticated which is beyond the scope of this study. However, the calculation of vorticity
with data from numerical simulations is often found in the literature (Gerz et al., 1994; Kanda
and Hino, 1994; Dupont et al., 2008; Finnigan et al., 2009; Dupont and Brunet, 2009).
That said, is presented the Fig 10 which shows the vertical profile of vorticity in its
three axes, which are arranged: i) along the mean flow direction (ωx); ii) perpendicular to the
mean flow direction (ωy); and iii) vertical direction (ωz). It is possible to see that ωx, ωy and
ωz are larger in the canopy top region, reducing its values upwards and downwards from this
region. Similar results have been found by researchers using LES to simulate the turbulent
flow over forests (Kanda and Hino, 1994; Finnigan et al., 2009; Dupont and Brunet, 2009).
Moreover, it is noted that at the treetop ωy vorticity is greater than the ones in the other two
directions, suggesting that the dominant features present vortex rotation axis perpendicular to
the direction of the dominant flow.
Fig. 10. Vertical profile of vorticity in the x, y and z directions.
4.7. Discussion.
In this work we used the LES to simulate the main features of turbulent flow, under
neutral conditions, in a region with characteristics similar to those of the Amazonian
rainforest. It is observed that in such situation, numerical flow simulation is capable to
creating an inflection point in the vertical wind profile located at canopy top (Fig. 4a).
95
According to Kanda and Hino (1994), near the canopy top the inflection points in vertical
profiles of wind velocity are continuously present on the flow due to the existing balance
between pressure gradient and the drag generated by the canopy. Dupont and Brunet (2009)
report that the development of an inflection point at canopy top leads to the Kelvin-Helmholtz
instability, and as result, the presence of predominantly two-dimensional eddies in the form of
rolls with axes of symmetry perpendicular the direction of the mean flow. As a consequence,
they start to populate the flow near the treetop, in the so-called roughness sub-layer. In this
research, in addition to obtaining realistic simulation of vertical profile of wind speed above
and within the canopy, also has been researched the vorticity field in the region near the
canopy top. The three components of the vorticity (𝜔) have been simulated. 𝜔𝑥 , 𝜔𝑦 and 𝜔𝑧
are the components of 𝜔 in the direction of the mean flow (U), transverse to U and vertical,
respectively. As a result, there is the interesting fact that 𝜔𝑦 at canopy top is greater than 𝜔𝑥
and 𝜔𝑧 (Fig. 10). This greater 𝜔𝑦 value suggests that the vortices above the Amazonian
rainforest are arranged in a way perpendicular to the mean flow (Robinson, 1991; Raupach et
al., 1996; Finnigan et al., 2009). Furthermore, the maximum values found for the momentum
flux (Fig. 5a), the values of 𝑟𝑤𝑢 (Fig. 7) and the turbulent intensities (σu and σw) in the region
close to the canopy top (Fig 5b) would be connected among them generating rolls in forestatmosphere interface in a similar way, as obtained by different authors in their studies
concerning the flow over different types of tall vegetation (Kanda and Hino, 1994; Dupont et
al.; 2008; Dupont and Brunet, 2009; Finnigan et al., 2009). It is also observed that near the
canopy top, the occurrence of sweeps and ejections are practically equal in number (Fig. 6).
This result confirms the findings of Kanda and Hino (1994), which found that in regions in
which the like-roll structures occur, the generated sweeps and ejections have similar
intensities.
Some researchers suggest that eddies generated above the canopy have a tilted
elliptical shape (Ho and Huerre, 1984; Kanda and Hino, 1994; Dupont and Brunet 2009), as
well shown by Dupont and Brunet (2009), pp 122, this tilted shape should help to explain the
spatial distribution of sweep and ejection along the flow, while the elliptical shape of the
eddies would be responsible for the existence of a momentum flux balance in this region. Ho
and Huerre (1984) report that if the existing eddies would present circular shapes, there would
be no dynamic conditions for the existence of momentum flux.
96
5. Conclusions
In this work we used the LES to simulate the turbulent flow within and above a
forested region with surface roughness characteristics similar to those of the Amazonian
rainforest. It was decided to simulate the flow under near neutral conditions. Unlike other
studies that have used several parameterizations for represent turbulent exchanges in the LES
in order to simulate the flow above a forest, in this study it is used only a drag force
associated to a vertical profile of LAI to represent the Amazonian rainforest canopy. Such
choice is based on the experimental evidence that in the roughness sublayer above the
Amazonian rainforest, mechanical forces are the main generator of turbulent kinetic energy.
As interesting results to mention, it is shown that the model used in this work represented
fairly well the characteristics of turbulent flow within and above the Amazonian rainforest,
what is presented in several analyses. It is observed that the modeled vertical profiles of
statistical moments of first, second and third order are quite close to those found with
experimental data. Furthermore, it was shown that the turbulent flow immediately above the
canopy is populated by structures which are organized with symmetry axis perpendicular to
the mean flow, known in the literature as rolls.
Acknowledgements
The authors would like to thank all people which directly or indirectly contributed to
the fulfillment of the 1999 LBA-Intensive wet Campaign, and the support of the university in
Ji-Paraná (UNIR), Instituto Brasileiro do Meio Ambiente e dos Recursos Naturais Renováveis
(IBAMA) and Instituto Nacional de Colonização e Reforma Agrária (INCRA). This work was
done under the LBA project framework, sponsered by the European Union, NASA, and
Brazilian Agencies as the Conselho Nacional de Pesquisa e Desenvolvimento Tecnológico
(CNPq) and the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP, process
01/06908-7). Cléo Dias-Junior is particularly grateful to CAPES for his PhD grant. Leonardo
Sá is particularly grateful to CNPq for his research grant (process 303.728/2010-8). Edson
Marques Filho is particularly grateful to CNPq for his research grant (process 308597/20125).
References
Abry, P., 1997. Ondelettes et turbulences: multirésolutions, algorithmes de décomposition,
invariance d'échelle et signaux de pression, ed. Diderot, Paris.
97
Andreae, M.O., Artaxo, P., Brandão, C., Carswell, F.E., Ciccioli, P., Costa, A.L., Culf, A.D.,
Esteves, J.L, Gash, J.H.C., Grace, J., Kabat, P., Lelieveld, J., Malhi, Y., Manzi, A.O.,
Meixner, F.X., Nobre, A.D., Nobre, C., Ruivo, M.L.P., Silva Dias, M.A., Stefani, P.,
Valentini, R., von Jouanne, J., Waterloo, M.J., 2002. Biogeochemical cycling ofcarbon,
water, energy, trace gases, and aerosols in Amazonia: the LBA-EUSTACH
experiments. Journal of Geophysical Research. 33,1–25.
Aris, R., 1989. Vectors, Tensors and the Basic Equations of Fluid Mechanics, ed. Dover, New
York.
Avissar, R., Nobre, C.A., 2002. Preface to special issue on the Large‐Scale Biosphere‐
Atmosphere Experiment in Amazonia (LBA). Journal of Geophysical Research:
Atmospheres (1984–2012), 107(D20), LBA-1.
Baldocchi, D.D., Meyers, T.P., 1988. Turbulence structure in a deciduous forest. BoundaryLayer Meteorology, 43(4), 345-364.
Betts, A. K., 2004. Understanding hydrometeorology using global models. Bulletin of the
American Meteorological Society, 85: 1673-1688.
Betts, A.K., Fisch, G., Von Randow, C., Silva Dias, M.A.F., Cohen, J.C.P., Da Silva, R.,
Fitzjarrald, D.R., 2009. The Amazonian boundary layer and mesoscale circulations.
Amazonia and Global Change, 163-181.
Brunet, Y., Finnigan, J.J., Raupach, M.R., 1994. A wind tunnel study of air flow in waving
wheat: single-point velocity statistics. Boundary-Layer Meteorology, 70(1-2), 95-132.
Courant, R., Friedrichs, K., Lewy, H., 1967. On the partial difference equations of
mathematical physics. IBM journal of Research and Development,11 (2), 215-234.
da Silva, R.R., Gandu, A.W., Sá, L.D., Dias, M.A.S., 2011. Cloud streets and land–water
interactions in the Amazon. Biogeochemistry, 105(1-3), 201-211.
de Souza, C.M., Dias-Junior, C.Q., Tóta, J., Sá, L.D.A., 2015. An empirical-analytic model to
describe the vertical wind speed profile above and within amazon forest. Meteorological
Applications. Submeted article.
Deardorff, J.W., 1972. Numerical investigation of neutral and unstable planetary boundary
layers. Journal of the Atmospheric Sciences, 29:91-115.
Dias-Junior, C.Q., Sá, L.D.A., Pachêco, V.B., de Souza, C.M., 2013. Coherent structures
detected in the unstable atmospheric surface layer above the Amazon forest. Journal of
Wind Engineering and Industrial Aerodynamics, 115, 1-8.
Dupont, S., Brunet, Y., 2009. Coherent structures in canopy edge flow: a large-eddy
simulation study. Journal of Fluid Mechanics, 630, 93-128.
98
Dupont, S., Brunet, Y., Finnigan, J.J., 2008. Large‐eddy simulation of turbulent flow over a
forested hill: Validation and coherent structure identification. Quarterly Journal of the
Royal Meteorological Society, 134(636), 1911-1929.
Dupont, S., Patton, E.G., 2012. Influence of stability and seasonal canopy changes on
micrometeorology within and above an orchard canopy: The CHATS experiment.
Agricultural and Forest Meteorology, 157, 11-29.
Edburg, S.L., Stock, D., Lamb, B.K., Patton, E.G., 2012. The effect of the vertical source
distribution on scalar statistics within and above a forest canopy. Boundary-layer
meteorology, 142 (3), 365-382.
Feynman R.P., Leighton R.B., Sands M., 1964. Lectures on Physics I. Addison - Wesley.
Finnigan, J., 2000. Turbulence in plant canopies. Annual Review of Fluid Mechanics, 32(1),
519-571.
Finnigan, J.J., Shaw, R.H., Patton, E.G., 2009. Turbulence structure above a vegetation
canopy. Journal of Fluid Mechanics, 637, 387-424.
Fitzjarrald, D.R., Moore, K.E., Cabral, O.M., Scolar, J., Manzi, A.O., Sá, L.D.A., 1990.
Daytime turbulent exchange between the Amazon forest and the atmosphere. Journal of
Geophysical Research: Atmospheres (1984–2012), 95(D10), 16825-16838.
Gao, W., Shaw, R.H., 1989. Observation of organized structure in turbulent flow within and
above a forest canopy. In Boundary Layer Studies and Applications (pp. 349-377).
Springer Netherlands.
Garstang, M., Fitzjarrald, D.R., 1999. Observations of surface to atmosphere interactions in
the tropics. Oxford University Press.
Gerz, T., Howell, J., Mahrt, L., 1994. Vortex structures and microfronts. Physics of Fluids 3
1242-151.
Griffin, O.M., 1981. Universal Similarity in the Wakes and Vibrating Bluff Structures.
Journal of Fluids Engineering, 103, 1: 52-58.
Ho, C. M., & Huerre, P. (1984). Perturbed free shear layers. Annual Review of Fluid
Mechanics, 16(1), 365-422.
Högström, U., 1990. Analysis of turbulence structure in the surface layer with a modified
similarity formulation for near neutral conditions. Journal of the atmospheric sciences,
47(16), 1949-1972.
Jackson, P.S., 1981. On the displacement height in the logarithmic velocity profile. Journal of
Fluid Mechanics, 111, pp 15-25 doi:10.1017/S0022112081002279.
99
Kanda, M., Hino, M., 1994. Organized structures in developing turbulent flow within and
above a plant canopy, using a large eddy simulation. Boundary-Layer Meteorology,
68(3), 237-257.
Katul, G.G., Albertson, J.D., 1998. An Investigation of Higher-Order Closure Models for a
Forested Canopy. Boundary-Layer Meteorology, 89, 1: 47-74.
Katul, G.G., Albertson, J.D., Parlange, M.B., Hsieh, C.I., Conklin, P.S., Sigmon, J.T., Knoerr,
K.R., 1996. The “inactive” eddy motion and the large-scale turbulent pressure
fluctuations in the dynamic sublayer. Journal of the atmospheric sciences. 53(17),
2512-2524.
Katul, G.G., Chang, W.H., 1999. Principal length scales in second-order closure models for
canopy turbulence. Journal of Applied Meteorology, 38(11), 1631-1643.
Kruijt, B., Malhi, Y., Lloyd, J., Norbre, A.D., Miranda, A.C., Pereira, M.G.P., Grace, J. 2000.
Turbulence statistics above and within two Amazon rain forest canopies. BoundaryLayer Meteorology, 94(2), 297-331.
Launiainen, S., Vesala, T., Mölder, M., Mammarella, I., Smolander, S., Rannik, Ü., Katul,
G.G., 2007. Vertical variability and effect of stability on turbulence characteristics
down to the floor of a pine forest. Tellus B, 59 (5), 919-936.
Lee, X., Black, T.A., 1993. Atmospheric turbulence within and above a Douglas-fir stand.
Part I: statistical properties of the velocity field. Boundary-Layer Meteorology, 64(1-2),
149-174.
Leonard, A., 1974. Energy cascade in large-eddy simulations of turbulent fluid flows. In
Turbulent Diffusion in Environmental Pollution (Vol. 1, pp. 237-248).
Lumley, J. L., Panofsky, H. A., 1964. The Structure of Atmospheric Turbulence. Wiley, 239
pp., New York.
Malhi, Y., Baker, T.R., Phillips, O.L., Almeida, S., Alvarez, E., Arroyo, L., ..., Lloyd, J.,
2004. The above‐ground coarse wood productivity of 104 Neotropical forest plots.
Global Change Biology, 10(5), 563-591.
Marques Filho, A.D.O., Dallarosa, R.G., Pachêco, V.B., 2005. Radiação solar e distribuição
vertical de área foliar em floresta Reserva Biológica do Cuieiras ZF2, Manaus. Acta
Amazônica, 35(4), 427-436.
Marshall, B. J., Wood, C. J., Gardiner, B. A., & Belcher, R. E. (2002). Conditional sampling
of forest canopy gusts. Boundary-Layer Meteorology, 102 (2), 225-251.
100
Maruyama, T., Rodi, W., Maruyama, Y., Hiraoka, H., 1999. Large eddy simulation of the
turbulent boundary layer behind roughness elements using an artificially generated
inflow. Journal of Wind Engineering and Industrial Aerodynamics, 83, 1–3, 381-392.
McNaughton, K.G., Laubach, J., 2000. Power spectra and cospectra for wind and scalars in a
disturbed surface layer at the base of an advective inversion. Boundary-layer
meteorology, 96(1-2), 143-185.
Mesinger, F., Arakawa, A., 1976. Numerical Methods Used in Atmospheric Models. Volume
I, Global Atmospheric Research Programme (GARP), WMO-ICSU Joint Organization
Committee, GARP publications Series, No 17, 292 pp.
Meyers, T.P., Baldocchi, D.D., 1991. The budgets of turbulent kinetic energy and Reynolds
stress within and above a deciduous forest. Agricultural and forest meteorology, 53(3),
207-222.
Moeng, C.H., 1984. A large-eddy-simulation model for the study of planetary boundary-layer
turbulence. Journal of the Atmospheric Sciences, 41(13), 2052-2062.
Moeng, C.H., Sullivan, P.P., 1994. A comparison of shear-and buoyancy-driven planetary
boundary layer flows. Journal of the Atmospheric Sciences, 51(7), 999-1022.
Oliveira, P.J., Fisch, G., 2000. Efeitos da Turbulência na Camada Limite Atmosférica em
áreas de Floresta e Pastagem na Amazônia. Revista Brasileira de Meteorologia, 15(2):
39–44.
Patton, E. G., Sullivan, P.P., Davis, K.J., 2003. The influence of a forest canopy on top‐down
and bottom‐up diffusion in the planetary boundary layer. Quarterly Journal of the Royal
Meteorological Society, 129 (590), 1415-1434.
Poggi, D., Katul,G.G., 2007. Turbulent flows on forested hilly terrain: the recirculation
region. Quarterly Journal of the Royal Meteorological Society, 133(625), 1027-1039.
Pope, S.B., 2004. Ten questions concerning the large-eddy simulation of turbulent flows. New
journal of Physics, 6 (1), 35.
Raupach, M.R., 1981. Conditional statistics of Reynolds stress in rough-wall and smooth-wall
turbulent boundary layers. Journal of Fluid Mechanics, 108, 363-382.
Raupach, M.R., Finnigan, J.J., Brunet, Y., 1996. Coherent Eddies and Turbulence in
Vegetation Canopies: The Mixing-layer Analogy. Boundary-Layer Meteorology, 78,
Raupach, M.R., Thom, A.S., 1981. Turbulence in and above plant canopies. Annual Review of
Fluid Mechanics, 13(1), 97-129.
Restrepo-Coupe, N., da Rocha, H.R., Hutyra L.R., Alessandro C. Araujo, A.C., Borma, L.S.,
Christoffersen, B., Cabral, O.M.R., de Camargo, P.B., Cardoso, F.L., Lola da Costa,
101
A.C., Fitzjarrald, D.R., Goulden, M.L., Kruijt, B., Maia, J.M.F., Malhi, Y.S., Manzi,
A.O., Miller, S.D., Nobre, A.D., von Randow, C., Sá, L.D.A., Sakai, R.K., Tota, J.,
Wofsy, S.C., Zanchi, F.B., Saleska, S.R., 2013. What drives the seasonality of
photosynthesis across the Amazon basin? A cross-site analysis of eddy flux tower
measurements from the Brasil flux network. Agricultural and Forest Meteorology, 182,
128-144.
Sá, L.D.A., Pachêco, V.B., 2006. Wind velocity above and inside Amazonian Rain Forest in
Rondônia. Revista Brasileira de Meteorologia, 21(3a), 50-58.
Sagaut, P., Deck, S., Terracol, M., 2006. Multiscale and multiresolution approaches in
turbulence (pp. 294-319). London: Imperial College Press.
Schlegel, F., Stiller, J., Bienert, A., Maas, H.G., Queck, R., Bernhofer, C., 2014. Large-eddy
simulation study of the effects on flow of a heterogeneous forest at sub-tree resolution.
Boundary-Layer Meteorology, 1-30.
Shaw, R.H., Den Hartog, G., Neumann, H.H., 1988. Influence of foliar density and thermal
stability on profiles of Reynolds stress and turbulence intensity in a deciduous forest.
Boundary-Layer Meteorology, 45(4), 391-409.
Shaw, R.H., Schumann, U., 1992. Large-eddy simulation of turbulent flow above and within a
forest. Boundary-Layer Meteorology, 61(1-2), 47-64.
Shaw, R.H., Tavangar, J., Ward, D.P., 1983. Structure of the Reynolds stress in a canopy
layer. Journal of climate and applied meteorology, 22(11), 1922-1931.
Shen, S., Leclerc, M.Y., 1997. Modelling the turbulence structure in the canopy layer.
Agricultural and Forest Meteorology, 87(1), 3-25.
Silva Dias, M.A.F.S., Rutledge, S., Kabat, P., Silva Dias, P., Nobre, C., Fisch, G., Dolman,
H., Zipser, E., Garstang, M., Manzi, A., Fuentes, J., Rocha, H., Marengo, J., PlanaFattori, A., Sa, L.D.A., Avala, R.C.S., Andreae, M., Artaxo, P., Gielow, R., Gatti, L.,
2002. Clouds and rain processes in a biosphere atmosphere interaction context in the
Amazon region. Journal of Geophysical Research, 20, 1–46.
Smagorinsky, J., 1984: Some Historical Remarks on the Use of Nonlinear Viscosities. In:
Large Eddy Simulation of Complex Engineering and Geophysical Flows.
Sorbjan Z., 1989. Structure of the Atmospheric Boundary Layer. Prentice-Hall, 317 pp.,
London.
Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology, Kluwer, 666 pp.,
Dordrecht.
102
Su, H.B., Shaw, R.H., Paw, K.T., Moeng, C.H., Sullivan, P.P., 1998. Turbulent statistics of
neutrally stratified flow within and above a sparse forest from large-eddy simulation
and field observations. Boundary-Layer Meteorology, 88(3), 363-397.
Tennekes, H., 1985. A Comparative Pathology of Atmospheric Turbulence in Two and Three
Dimensions, In: Ghil, M., Benzi R., Parisi G., Turbulence and Predictability in
Geophysical Fluid Dynamics and Climate Dynamics, Ed. North-Holland Physics
Publishing, Amsterdam pp. 45-70.
Townsend, A.A., 1976. The Structure of Turbulent Shear Flow. ed. Cambridge UniversityPress, Cambridge.
Vilà‐Guerau de Arellano, J., Patton, E.G., Karl, T., van den Dries, K., Barth, M.C., Orlando,
J.J., 2011. The role of boundary layer dynamics on the diurnal evolution of isoprene and
the hydroxyl radical over tropical forests. Journal of Geophysical Research:
Atmospheres (1984–2012), 116(D7).
Von Randow, C., Manzi, A.O., Kruijt, B., De Oliveira, P.J., Zanchi, F.B., Silva, R.L., Kabat,
P., 2004. Comparative measurements and seasonal variations in energy and carbon
exchange over forest and pasture in South West Amazonia. Theoretical and Applied
Climatology, 78(1-3), 5-26.
von Randow, C., Sá, L.D., Gannabathula, P.S., Manzi, A.O., Arlino, P.R., Kruijt, B., 2002.
Scale variability of atmospheric surface layer fluxes of energy and carbon over a
tropical rain forest in southwest Amazonia 1. Diurnal conditions. Journal of
Geophysical Research: Atmospheres (1984–2012), 107(D20), LBA-29.
Zeri M., Sá L.D.A., Manzi A.O., Araújo A.C., Aguiar R.G., von Randow C, Sampaio G.,
Cardoso F.L. Nobre C.A., 2014. Variability of Carbon and Water Fluxes Following
Climate Extremes over a Tropical Forest in Southwestern Amazonia, PLOS ONE, 9, 2:
e88130.
Zeri, M., Sá, L.D.A., 2010. The impact of data gaps and quality control filtering on the
balances of energy and carbon for a Southwest Amazon forest. Agricultural and forest
meteorology, 150(12), 1543-1552.
Zeri, M., Sá, L.D.A., 2011. Horizontal and vertical turbulent fluxes forced by a gravity wave
event in the nocturnal atmospheric surface layer over the Amazon forest. Boundarylayer meteorology, 138(3), 413-431.
103
CONCLUSÕES
Foram usadas as facilidades oferecidas por uma torre de 67m de altura instalada na
Amazônia ocidental, na reserva florestal Rebio-Jarú, em Rondônia. A organização dos
instrumentos na torre favoreceu a investigação da variabilidade da altura do ponto de inflexão
no perfil vertical do vento. Tal investigação facilitou a pesquisa de alguns aspectos da
estrutura da turbulência atmosférica durante os períodos diurno e noturno acima da RebioJarú.
Dentre os principais resultados do período diurno destacam-se: i) um modelo
empírico-analítico capaz de descrever o perfil vertical de velocidade do vento acima e dentro
da floresta amazônica. Esta formulação, fundamentada em parâmetros básicos tais como a
altura do ponto de inflexão do perfil vertical do vento, o índice de área foliar, proporcionou
um melhor ajuste para os dados experimentais medidos tanto acima quanto dentro do dossel;
ii) uma correlação estatisticamente robusta entre a escala temporal de ocorrência das
estruturas coerentes e a altura do ponto de inflexão. Tais resultados são importantes para
melhorar o entendimento acerca da subcamada rugosa além de permitir parametrizações mais
realistas dos processos de trocas entre a floresta e a atmosfera.
Para a camada limite noturna observou-se que os maiores valores da altura do ponto de
inflexão estavam relacionados a situações em que era possível observar a existência de um
vórtice turbulento dominante, imediatamente acima do dossel florestal. Tal vórtice, sob certas
circunstâncias, desempenha um papel ativo nos processos de troca entre floresta-atmosfera.
Outro resultado encontrado foi à existência de regimes turbulentos noturnos com
características diferentes (taxa de dissipação de energia cinética turbulenta, escala de
comprimento de cisalhamento do vento, escala temporal das estruturas coerentes, dentre
outros), e que são influenciados pela altura do ponto de inflexão. Outro resultado importante
foi: a) regimes de vento fraco são muito mais frequentes no período noturno; b) regimes de
vento forte ou situações marcadamente não estacionárias ocorrem durante curtos intervalos de
tempo. Entretanto, nestes regimes de ventos fracos os fluxos turbulentos são
aproximadamente uma ordem de magnitudes maiores que aqueles onde os ventos são fracos.
Além dos resultados encontrados com dados experimentais, recorreu-se também a
simulação dos grandes turbilhoes (Large eddy simulation - LES) para uma melhor
compreensão de algumas características do escoamento turbulento acima de superfícies
rugosas, tal como a floresta amazônica. Inseriu-se no LES uma força de arrasto representativa
da Rebio-Jarú. Observou-se que o modelo simulou bem o escoamento turbulento acima e
104
dentro da floresta amazônica. Os perfis verticais modelados dos momentos estatísticos de
primeira, segunda e terceira ordem foram muito próximos dos resultados mostrados na
literatura, para dados experimentais. Além disso, mostrou-se que o escoamento turbulento
imediatamente
acima
do
dossel
é
povoado
por
estruturas
que
se
organizam
perpendicularmente a direção do escoamento médio, conhecidas, na literatura, como
estruturas em forma de rolos.
REFERÊNCIAS BIBLIOGRÁFICAS
Acevedo, O. C.; Fitzjarrald, D. R. 2003. In the Core of the Night - Effects of Intermittent
Mixing on a Horizontally Heterogeneous Surface. Boundary-Layer Meteorology, 106:133.
Acevedo, O. C.; Moraes, O. L. L.; Degrazia, G. A.; Fitzjarrald, D. R.; Manzi, A. O.; Campos,
J. G. 2009. Is friction velocity the most appropriate scale for correcting nocturnal carbon
dioxide fluxes? Agricultural and Forest Meteorology, 149:1-10.
Araújo, A. C.; Dolman, A. J.; Waterloo, M. J.; Gash, J. H. C.; Kruijt, B.; Zanchi, F. B.;
Lange, J. M. E.; Stoevelaar, R.; Manzi, A. O.; Nobre, A. D.; Lootens R. N.; Backer, J.
2010. The spatial variability of CO2 storage and the interpretation of eddy covariance
fluxes in central Amazonia. Agricultural and Forest Meteorology, 150: 226-237.
Belušić, D.; Mahrt L. 2012. Is geometry more universal than physics in atmospheric boundary
layer flow? J. Geophys. Res.,117, D09115.
Brunet Y.; Irvine, M. R. 2000. The Control of Coherent Eddies in Vegetation Canopies:
Streamwise Structure Spacing, Canopy Shear Scale and Atmospheric Stability.
Boundary-Layer Meteorology, 94(1): 139-163.
Campanharo, A. S. L. O.; Ramos, F. M.; Macau, E. E. N.; Rosa, R. R.; Bolzan M. J. A.; Sá, L.
D. A. 2008. Searching Chaos and Coherent Structures in the Atmospheric Turbulence
above Amazon Forest, Philosophical Transactions of the Royal Society of London A,
Mathematical and Physical Sciences, 366 (1865): 579-589.
Cava, D.; Giostra, U.; Siqueira, M.; Katul, G. 2004. Organised Motion and Radiative
Properties in the Nocturnal Canopy Sublayer above an Even-aged Pine Forest.
Boundary-Layer Meteorology, 112:129-157.
105
Cava, D.; Katul, G. G. 2008. Spectral Short-circuiting and Wake Production within the
Canopy Trunc Space of an Alpine Hardwood Forest. Boundary-Layer Meteorology,
126: 415-431.
Dias-Júnior, C. Q.; Sá, L. D. A.; Pachêco, V. B.; de Souza, C. M. 2013. Coherent structures
detected in the unstable atmospheric surface layer above the Amazon forest. Journal of
Wind Engineering & Industrial Aerodynamics 115: 1-8.
Doughty, C. E.; Goulden, M. L. 2008. Seasonal patterns of tropical forest leaf area index and
CO2 exchange. Journal of Geophysical Research: Biogeosciences (2005–2012),
113(G1).
Eder, F.; Serafimovich A.; Foken, T. 2013. Coherent Structures at a Forest Edge: Properties,
Coupling and Impact of Secondary Circulations. Boundary-Layer Meteorology, 148:
285-308.
Finnigan, J. J. 2000. Turbulence in plant canopies. Annual Review of Fluid Mechanics, 32:
519-571.
Finnigan, J. J.; Shaw R. H.; Patton, E. G. 2009. Turbulence structure above a vegetation
canopy, Journal of Fluid Mechanics, 637: 387-424.
Högström, U.; Bergström, H. 1996. Organized Turbulence in the Near-Neutral Atmospheric
Surface Layer. Journal of the Atmospheric Sciences, 53(17): 2452-2464.
Kruijt, B.; Malhi, Y.; Lloyd, J.; Norbre, A.D.; Miranda, A.C.; Pereira, M.G.P.; Grace, J. 2000.
Turbulence statistics above and within two Amazon rain forest canopies. BoundaryLayer Meteorology, 94(2), 297-331.
Mafra, A. C. B. 2014. Características das trocas turbulentas noturnas de CO2 entre a floresta
de Uatumã, Amazonas, e a atmosfera. Dissertação de Mestrado Universidade Federal do
Pará, Belém, Pará.
Mahrt, L. 1998. Stratified Atmospheric Boundary Layers and Breakdown of Models.
Theoretical and Computational Fluid Dynamics, 11: 263-279.
Mahrt, L. 1999. Stratified Atmospheric Boundary-Layers. Boundary-Layer Meteorology, 90:
(3): 375-396.
Mahrt, L. 2000. Surface Heterogeneity and Vertical Structure of the Boundary Layer.
Boundary-Layer Meteorology, 96 (1-2): 33-62.
Mahrt, L.; Sun, J.; Vickers, D.; MacPherson, J. I.; Pederson J. R.; Desjardins, R. L. 1994.
Observations of Fluxes and Inland Breezes over Heterogeneous Surface. Journal of the
Atmospheric Sciences, 51 (17): 2484-2499.
106
Marshall, B. J.; Wood, C. J.; Gardiner B. A.; Belcher, B. E. 2012. Conditional Sampling of
Forest Canopy Gusts, Boundary-Layer Meteorology, 102: 225-251.
Pachêco, V. B. 2001. Algumas Características do Acoplamento entre o Escoamento Acima e
Abaixo da Copa da Floresta Amazônica em Rondônia, INPE, São José dos Campos, SP,
Dissertação de Mestrado em Meteorologia, 109 pp.
Paw U, K. T.; Brunet, Y.; Collineau, S.; Shaw, R. H.; Maitani, T.; Qiu J.; Hipps, L. 1992. On
coherent structures in turbulence above and within agricultural plant canopies.
Agricultural and Forest Meteorology, 61 (1-2): 55-68.
Poulos, G. S.; Blumen, W.; Fritts, D. C.; Lundquist, J. K.; Sun, J.; Burns, S. P.; Nappo, C.;
Banta, R.; Newsom, R.; Cuxart, J.; Terradellas, E.; Balsley, B.; Jensen, M. 2002.
CASES-99: A comprehensive investigation of the stable nocturnal boundary layer.
Bulletin of the American Meteorological Society, 83(4): 555-581.
Princevac, M.; Hunt, J. C. R.; Fernando, H. J. S. 2008. Quasi-Steady Katabatic Winds on
Slopes in Wide Valleys: Hydraulic Theory and Observations. Journal of the
Atmospheric Sciences, 65: 627-643.
Raupach, M. R.; Finnigan, J. J.; Brunet, Y. 1996. Coherent Eddies and Turbulence in
Vegetation Canopies: The Mixing-layer Analogy. Boundary-Layer Meteorology, 78(34): 351-382.
Robinson, S. K. 1991. Coherent Motions in the Turbulent Boundary Layer. Annual Rev.of
Fluid Mechanics, 23: 601-639.
Sá L. D. A., Pachêco, V. B. 2006. Wind Velocity above and inside Amazonian Rain Forest in
Rondonia., Revista Brasileira de Meteorologia, 21 (3a): 50-58.
Stewart R. W. 1969. Turbulence and waves in a stratified atmosphere, Radio Science, 4 (12):
1269-1278.
Sun, J.; Burns, S. P.; Lenschow, D. H.; Banta, R.; Newsom, B.; Coulter, R.; Frasier, S.; Ince,
T.; Nappo, C.; Cuxart, J.; Blumen, W.; Delany, A. C.; Lee X.; Hu, X.-Z. 2002.
Intermittent Turbulence Associated with a Density Current Passage in the Stable
Boundary Layer, Boundary-Layer Meteorology, 105: 199-219.
Sun, J.; Mahrt, L.; Banta, R. M.; Pichugina, Y. L. 2012. Turbulence Regimes and Turbulence
Intermittency in the Stable Boundary Layer during CASES-99. Journal of the
Atmospheric Sciences, 69: 338-351.
Thomas, C.; Foken, T. 2007. Flux contribution of coherent structures and its implications for
the exchange of energy and matter in a tall spruce canopy. Boundary-Layer
Meteorology, 123: 317-337.
107
Turner, B. J.; Leclerc, M. Y.; Gauthier, M.; Moore K.; Fitzjarrald, D. R. 1994. Identification
of turbulent structures above a forest canopy using a wavelet transform. Journal of
Geophysical Research, 99 (D1): 1919-1926.
Van de Wiel, B. J. H.; Moene, A. F.; Hartogensis, O. K.; De Bruin H. A. R.; Holtslag, A. A.
M. 2003. Intermittent Turbulence in the Stable Boundary Layer over Land.Part III. A
Classification for Observations during CASES-99. Journal of the Atmospheric Sciences,
60: 2509-2522.
Van de Wiel, B. J. H.; Moene, A. F.; Ronda, R. J.; De Bruin H. A. R.; Holtslag, A. A. M.
2002b. Intermittent Turbulence and Oscillations in the Stable Boundary Layer over
Land. Part II. A System Dynamica Approach. Journal of the Atmospheric Sciences, 59:
2567-2581.
Van de Wiel, B. J. H.; Ronda, R. J.; Moene, A. F.; De Bruin H. A. R.; Holtslag, A. A. M.
2002a. Intermittent Turbulence and Oscillations in the Stable Boundary Layer over
Land. Part I. A Bulk Model. Journal of the Atmospheric Sciences, 59: 942-958.
Williams, C. A.; Scanlon, T. M.; Albertson, J. D. 2007. Influence of surface heterogeneity on
scalar dissimilarity in the roughness sublayer. Boundary-Layer Meteorology, 122:149165.
Yi, C. 2008. Momentum Transfer within Canopies. Journal of Applied Meteorology and
Climatology. 47: 262-275.
Zeri, M.; Sá L. D. A., Nobre, C. A. 2014. Contribution of coherent structures to the buoyancy
heat flux under different conditions of stationarity over Amazonian forest sites.
Atmospheric Science Letters, Doi: 10.1002/asl2.544.
Zeri, M.; Sá, L. D. A. 2011.Scale dependence of coherent structures contribution to the
daytime buoyancy heat flux over the Pantanal wetland, Brazil. Atmospheric Science
Letters, 12 (2): 200-206.
Zhang, R.; He, X.; Doolen, G.; Chen, S. 2001. Surface tension effects on two-dimensional
two-phase Kelvin-Helmholtz instabilities. Advances in Water Resources, 24(3-4): 461478.